Sensim Math · Depth 한국어

← 3-1 · AM and PM make a 24-hour day · Elapsed Time and Base-Sixty Regrouping

AM and PM make a 24-hour day · 10 practice problems

3.MD.A.1

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: 3 hours 45 minutes

Olia's family boarded a plane at the airport at 11:40 PM on Sunday and arrived at their destination the next day at 3:25 AM (departure-city time). How many hours and minutes long was Olia's family's flight?

Show solution

Understand

A flight left at 11:40 PM Sunday and landed at 3:25 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 11:40 PM to midnight, then from midnight to 3:25 AM.

Givens
  • Departure time: 11:40 PM Sunday
  • Arrival time: 3:25 AM the next day, in departure-city time
  • A full day is 24 hours: 12 hours of AM and 12 hours of PM
Unknowns
  • The flight duration in hours and minutes
Constraints
  • The flight crosses midnight, so the elapsed time spans from PM into the next AM
  • Both clock times are in the same time zone, so no zone adjustment is needed

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

Execute

#7 Identify Subproblems 3.MD.A.1
From 11:40 PM to 12:00 midnight is 0 hr 20 min.
12:00−11:40=0 hr 20 min12{:}00 - 11{:}40 = 0 \text{ hr } 20 \text{ min}
Midnight ends the PM half of the day, so it is the natural splitting point.
#7 Identify Subproblems 3.MD.A.1
From 12:00 midnight to 3:25 AM is simply 3 hr 25 min, since midnight is the start of the AM half.
3:25−12:00=3 hr 25 min3{:}25 - 12{:}00 = 3 \text{ hr } 25 \text{ min}
After midnight the clock reads the AM hours directly, so the second piece is read straight off.
#7 Identify Subproblems 3.MD.A.1
Add the two spans: 0 hr 20 min plus 3 hr 25 min. Minutes: 20 + 25 = 45 min. Hours: 0 + 3 = 3 hr. The total flight time is 3 hr 45 min.
0 hr 20 min+3 hr 25 min=3 hr 45 min0 \text{ hr } 20 \text{ min} + 3 \text{ hr } 25 \text{ min} = 3 \text{ hr } 45 \text{ min}
Adding the before-midnight and after-midnight pieces gives the whole elapsed time.
Answer: 3 hours 45 minutes

Review

From about 11 PM to about 3 AM is roughly 3 hours, and our exact answer of 3 hr 45 min fits that estimate. The minutes (45) stayed under 60, so no extra hour was carried, which is consistent.

Use 24-hour time (tool 15): 11:40 PM is 23:40 and 3:25 AM next day is 27:25; 27:25 - 23:40 = 3 hr 45 min, matching the split-at-midnight method.

Standards · min grade 3

  • 3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans
💡 When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!
Variant 2 answer: 7 hours 45 minutes

Mila's family boarded a plane at the airport at 10:50 PM on Sunday and arrived at their destination the next day at 6:35 AM (departure-city time). How many hours and minutes long was Mila's family's flight?

Show solution

Understand

A flight left at 10:50 PM Sunday and landed at 6:35 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 10:50 PM to midnight, then from midnight to 6:35 AM.

Givens
  • Departure time: 10:50 PM Sunday
  • Arrival time: 6:35 AM the next day, in departure-city time
  • A full day is 24 hours: 12 hours of AM and 12 hours of PM
Unknowns
  • The flight duration in hours and minutes
Constraints
  • The flight crosses midnight, so the elapsed time spans from PM into the next AM
  • Both clock times are in the same time zone, so no zone adjustment is needed

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

Execute

#7 Identify Subproblems 3.MD.A.1
From 10:50 PM to 12:00 midnight is 1 hr 10 min.
12:00−10:50=1 hr 10 min12{:}00 - 10{:}50 = 1 \text{ hr } 10 \text{ min}
Midnight ends the PM half of the day, so it is the natural splitting point.
#7 Identify Subproblems 3.MD.A.1
From 12:00 midnight to 6:35 AM is simply 6 hr 35 min, since midnight is the start of the AM half.
6:35−12:00=6 hr 35 min6{:}35 - 12{:}00 = 6 \text{ hr } 35 \text{ min}
After midnight the clock reads the AM hours directly, so the second piece is read straight off.
#7 Identify Subproblems 3.MD.A.1
Add the two spans: 1 hr 10 min plus 6 hr 35 min. Minutes: 10 + 35 = 45 min. Hours: 1 + 6 = 7 hr. The total flight time is 7 hr 45 min.
1 hr 10 min+6 hr 35 min=7 hr 45 min1 \text{ hr } 10 \text{ min} + 6 \text{ hr } 35 \text{ min} = 7 \text{ hr } 45 \text{ min}
Adding the before-midnight and after-midnight pieces gives the whole elapsed time.
Answer: 7 hours 45 minutes

Review

From about 10 PM to about 6 AM is roughly 7 hours, and our exact answer of 7 hr 45 min fits that estimate. The minutes (45) stayed under 60, so no extra hour was carried, which is consistent.

Use 24-hour time (tool 15): 10:50 PM is 22:50 and 6:35 AM next day is 30:35; 30:35 - 22:50 = 7 hr 45 min, matching the split-at-midnight method.

Standards · min grade 3

  • 3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans
💡 When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!
Variant 3 answer: 8 hours 20 minutes

Ezra's family boarded a plane at the airport at 8:45 PM on Sunday and arrived at their destination the next day at 5:05 AM (departure-city time). How many hours and minutes long was Ezra's family's flight?

Show solution

Understand

A flight left at 8:45 PM Sunday and landed at 5:05 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 8:45 PM to midnight, then from midnight to 5:05 AM.

Givens
  • Departure time: 8:45 PM Sunday
  • Arrival time: 5:05 AM the next day, in departure-city time
  • A full day is 24 hours: 12 hours of AM and 12 hours of PM
Unknowns
  • The flight duration in hours and minutes
Constraints
  • The flight crosses midnight, so the elapsed time spans from PM into the next AM
  • Both clock times are in the same time zone, so no zone adjustment is needed

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

Execute

#7 Identify Subproblems 3.MD.A.1
From 8:45 PM to 12:00 midnight is 3 hr 15 min.
12:00−8:45=3 hr 15 min12{:}00 - 8{:}45 = 3 \text{ hr } 15 \text{ min}
Midnight ends the PM half of the day, so it is the natural splitting point.
#7 Identify Subproblems 3.MD.A.1
From 12:00 midnight to 5:05 AM is simply 5 hr 5 min, since midnight is the start of the AM half.
5:05−12:00=5 hr 5 min5{:}05 - 12{:}00 = 5 \text{ hr } 5 \text{ min}
After midnight the clock reads the AM hours directly, so the second piece is read straight off.
#7 Identify Subproblems 3.MD.A.1
Add the two spans: 3 hr 15 min plus 5 hr 5 min. Minutes: 15 + 5 = 20 min. Hours: 3 + 5 = 8 hr. The total flight time is 8 hr 20 min.
3 hr 15 min+5 hr 5 min=8 hr 20 min3 \text{ hr } 15 \text{ min} + 5 \text{ hr } 5 \text{ min} = 8 \text{ hr } 20 \text{ min}
Adding the before-midnight and after-midnight pieces gives the whole elapsed time.
Answer: 8 hours 20 minutes

Review

From about 8 PM to about 5 AM is roughly 8 hours, and our exact answer of 8 hr 20 min fits that estimate. The minutes (20) stayed under 60, so no extra hour was carried, which is consistent.

Use 24-hour time (tool 15): 8:45 PM is 20:45 and 5:05 AM next day is 29:05; 29:05 - 20:45 = 8 hr 20 min, matching the split-at-midnight method.

Standards · min grade 3

  • 3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans
💡 When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!
Variant 4 answer: 10 hours 45 minutes

Aria's family boarded a plane at the airport at 9:05 PM on Sunday and arrived at their destination the next day at 7:50 AM (departure-city time). How many hours and minutes long was Aria's family's flight?

Show solution

Understand

A flight left at 9:05 PM Sunday and landed at 7:50 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 9:05 PM to midnight, then from midnight to 7:50 AM.

Givens
  • Departure time: 9:05 PM Sunday
  • Arrival time: 7:50 AM the next day, in departure-city time
  • A full day is 24 hours: 12 hours of AM and 12 hours of PM
Unknowns
  • The flight duration in hours and minutes
Constraints
  • The flight crosses midnight, so the elapsed time spans from PM into the next AM
  • Both clock times are in the same time zone, so no zone adjustment is needed

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

Execute

#7 Identify Subproblems 3.MD.A.1
From 9:05 PM to 12:00 midnight is 2 hr 55 min.
12:00−9:05=2 hr 55 min12{:}00 - 9{:}05 = 2 \text{ hr } 55 \text{ min}
Midnight ends the PM half of the day, so it is the natural splitting point.
#7 Identify Subproblems 3.MD.A.1
From 12:00 midnight to 7:50 AM is simply 7 hr 50 min, since midnight is the start of the AM half.
7:50−12:00=7 hr 50 min7{:}50 - 12{:}00 = 7 \text{ hr } 50 \text{ min}
After midnight the clock reads the AM hours directly, so the second piece is read straight off.
#7 Identify Subproblems 3.MD.A.1
Add the two spans: 2 hr 55 min plus 7 hr 50 min. Minutes: 55 + 50 = 105 min (carry 1 hr). Hours: 2 + 7 + 1 = 10 hr. The total flight time is 10 hr 45 min.
2 hr 55 min+7 hr 50 min=10 hr 45 min2 \text{ hr } 55 \text{ min} + 7 \text{ hr } 50 \text{ min} = 10 \text{ hr } 45 \text{ min}
Adding the before-midnight and after-midnight pieces gives the whole elapsed time.
Answer: 10 hours 45 minutes

Review

From about 9 PM to about 7 AM is roughly 10 hours, and our exact answer of 10 hr 45 min fits that estimate. The minutes (45) stayed under 60 after one carry, which is consistent.

Use 24-hour time (tool 15): 9:05 PM is 21:05 and 7:50 AM next day is 31:50; 31:50 - 21:05 = 10 hr 45 min, matching the split-at-midnight method.

Standards · min grade 3

  • 3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans
💡 When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!
Variant 5 answer: 7 hours 15 minutes

Emma's family boarded a plane at the airport at 10:30 PM on Sunday and arrived at their destination the next day at 5:45 AM (departure-city time). How many hours and minutes long was Emma's family's flight?

Show solution

Understand

A flight left at 10:30 PM Sunday and landed at 5:45 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 10:30 PM to midnight, then from midnight to 5:45 AM.

Givens
  • Departure time: 10:30 PM Sunday
  • Arrival time: 5:45 AM the next day, in departure-city time
  • A full day is 24 hours: 12 hours of AM and 12 hours of PM
Unknowns
  • The flight duration in hours and minutes
Constraints
  • The flight crosses midnight, so the elapsed time spans from PM into the next AM
  • Both clock times are in the same time zone, so no zone adjustment is needed

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

Execute

#7 Identify Subproblems 3.MD.A.1
From 10:30 PM to 12:00 midnight is 1 hr 30 min.
12:00−10:30=1 hr 30 min12{:}00 - 10{:}30 = 1 \text{ hr } 30 \text{ min}
Midnight ends the PM half of the day, so it is the natural splitting point.
#7 Identify Subproblems 3.MD.A.1
From 12:00 midnight to 5:45 AM is simply 5 hr 45 min, since midnight is the start of the AM half.
5:45−12:00=5 hr 45 min5{:}45 - 12{:}00 = 5 \text{ hr } 45 \text{ min}
After midnight the clock reads the AM hours directly, so the second piece is read straight off.
#7 Identify Subproblems 3.MD.A.1
Add the two spans: 1 hr 30 min plus 5 hr 45 min. Minutes: 30 + 45 = 75 min (carry 1 hr). Hours: 1 + 5 + 1 = 7 hr. The total flight time is 7 hr 15 min.
1 hr 30 min+5 hr 45 min=7 hr 15 min1 \text{ hr } 30 \text{ min} + 5 \text{ hr } 45 \text{ min} = 7 \text{ hr } 15 \text{ min}
Adding the before-midnight and after-midnight pieces gives the whole elapsed time.
Answer: 7 hours 15 minutes

Review

From about 10 PM to about 5 AM is roughly 7 hours, and our exact answer of 7 hr 15 min fits that estimate. The minutes (15) stayed under 60 after one carry, which is consistent.

Use 24-hour time (tool 15): 10:30 PM is 22:30 and 5:45 AM next day is 29:45; 29:45 - 22:30 = 7 hr 15 min, matching the split-at-midnight method.

Standards · min grade 3

  • 3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans
💡 When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!
Variant 6 answer: 5 hours 25 minutes

Cora's family boarded a plane at the airport at 11:15 PM on Sunday and arrived at their destination the next day at 4:40 AM (departure-city time). How many hours and minutes long was Cora's family's flight?

Show solution

Understand

A flight left at 11:15 PM Sunday and landed at 4:40 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 11:15 PM to midnight, then from midnight to 4:40 AM.

Givens
  • Departure time: 11:15 PM Sunday
  • Arrival time: 4:40 AM the next day, in departure-city time
  • A full day is 24 hours: 12 hours of AM and 12 hours of PM
Unknowns
  • The flight duration in hours and minutes
Constraints
  • The flight crosses midnight, so the elapsed time spans from PM into the next AM
  • Both clock times are in the same time zone, so no zone adjustment is needed

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

Execute

#7 Identify Subproblems 3.MD.A.1
From 11:15 PM to 12:00 midnight is 0 hr 45 min.
12:00−11:15=0 hr 45 min12{:}00 - 11{:}15 = 0 \text{ hr } 45 \text{ min}
Midnight ends the PM half of the day, so it is the natural splitting point.
#7 Identify Subproblems 3.MD.A.1
From 12:00 midnight to 4:40 AM is simply 4 hr 40 min, since midnight is the start of the AM half.
4:40−12:00=4 hr 40 min4{:}40 - 12{:}00 = 4 \text{ hr } 40 \text{ min}
After midnight the clock reads the AM hours directly, so the second piece is read straight off.
#7 Identify Subproblems 3.MD.A.1
Add the two spans: 0 hr 45 min plus 4 hr 40 min. Minutes: 45 + 40 = 85 min (carry 1 hr). Hours: 0 + 4 + 1 = 5 hr. The total flight time is 5 hr 25 min.
0 hr 45 min+4 hr 40 min=5 hr 25 min0 \text{ hr } 45 \text{ min} + 4 \text{ hr } 40 \text{ min} = 5 \text{ hr } 25 \text{ min}
Adding the before-midnight and after-midnight pieces gives the whole elapsed time.
Answer: 5 hours 25 minutes

Review

From about 11 PM to about 4 AM is roughly 5 hours, and our exact answer of 5 hr 25 min fits that estimate. The minutes (25) stayed under 60 after one carry, which is consistent.

Use 24-hour time (tool 15): 11:15 PM is 23:15 and 4:40 AM next day is 28:40; 28:40 - 23:15 = 5 hr 25 min, matching the split-at-midnight method.

Standards · min grade 3

  • 3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans
💡 When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!
Variant 7 answer: 9 hours 50 minutes

Noah's family boarded a plane at the airport at 8:20 PM on Sunday and arrived at their destination the next day at 6:10 AM (departure-city time). How many hours and minutes long was Noah's family's flight?

Show solution

Understand

A flight left at 8:20 PM Sunday and landed at 6:10 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 8:20 PM to midnight, then from midnight to 6:10 AM.

Givens
  • Departure time: 8:20 PM Sunday
  • Arrival time: 6:10 AM the next day, in departure-city time
  • A full day is 24 hours: 12 hours of AM and 12 hours of PM
Unknowns
  • The flight duration in hours and minutes
Constraints
  • The flight crosses midnight, so the elapsed time spans from PM into the next AM
  • Both clock times are in the same time zone, so no zone adjustment is needed

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

Execute

#7 Identify Subproblems 3.MD.A.1
From 8:20 PM to 12:00 midnight is 3 hr 40 min.
12:00−8:20=3 hr 40 min12{:}00 - 8{:}20 = 3 \text{ hr } 40 \text{ min}
Midnight ends the PM half of the day, so it is the natural splitting point.
#7 Identify Subproblems 3.MD.A.1
From 12:00 midnight to 6:10 AM is simply 6 hr 10 min, since midnight is the start of the AM half.
6:10−12:00=6 hr 10 min6{:}10 - 12{:}00 = 6 \text{ hr } 10 \text{ min}
After midnight the clock reads the AM hours directly, so the second piece is read straight off.
#7 Identify Subproblems 3.MD.A.1
Add the two spans: 3 hr 40 min plus 6 hr 10 min. Minutes: 40 + 10 = 50 min. Hours: 3 + 6 = 9 hr. The total flight time is 9 hr 50 min.
3 hr 40 min+6 hr 10 min=9 hr 50 min3 \text{ hr } 40 \text{ min} + 6 \text{ hr } 10 \text{ min} = 9 \text{ hr } 50 \text{ min}
Adding the before-midnight and after-midnight pieces gives the whole elapsed time.
Answer: 9 hours 50 minutes

Review

From about 8 PM to about 6 AM is roughly 9 hours, and our exact answer of 9 hr 50 min fits that estimate. The minutes (50) stayed under 60, so no extra hour was carried, which is consistent.

Use 24-hour time (tool 15): 8:20 PM is 20:20 and 6:10 AM next day is 30:10; 30:10 - 20:20 = 9 hr 50 min, matching the split-at-midnight method.

Standards · min grade 3

  • 3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans
💡 When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!
Variant 8 answer: 6 hours 20 minutes

Liam's family boarded a plane at the airport at 9:55 PM on Sunday and arrived at their destination the next day at 4:15 AM (departure-city time). How many hours and minutes long was Liam's family's flight?

Show solution

Understand

A flight left at 9:55 PM Sunday and landed at 4:15 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 9:55 PM to midnight, then from midnight to 4:15 AM.

Givens
  • Departure time: 9:55 PM Sunday
  • Arrival time: 4:15 AM the next day, in departure-city time
  • A full day is 24 hours: 12 hours of AM and 12 hours of PM
Unknowns
  • The flight duration in hours and minutes
Constraints
  • The flight crosses midnight, so the elapsed time spans from PM into the next AM
  • Both clock times are in the same time zone, so no zone adjustment is needed

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

Execute

#7 Identify Subproblems 3.MD.A.1
From 9:55 PM to 12:00 midnight is 2 hr 5 min.
12:00−9:55=2 hr 5 min12{:}00 - 9{:}55 = 2 \text{ hr } 5 \text{ min}
Midnight ends the PM half of the day, so it is the natural splitting point.
#7 Identify Subproblems 3.MD.A.1
From 12:00 midnight to 4:15 AM is simply 4 hr 15 min, since midnight is the start of the AM half.
4:15−12:00=4 hr 15 min4{:}15 - 12{:}00 = 4 \text{ hr } 15 \text{ min}
After midnight the clock reads the AM hours directly, so the second piece is read straight off.
#7 Identify Subproblems 3.MD.A.1
Add the two spans: 2 hr 5 min plus 4 hr 15 min. Minutes: 5 + 15 = 20 min. Hours: 2 + 4 = 6 hr. The total flight time is 6 hr 20 min.
2 hr 5 min+4 hr 15 min=6 hr 20 min2 \text{ hr } 5 \text{ min} + 4 \text{ hr } 15 \text{ min} = 6 \text{ hr } 20 \text{ min}
Adding the before-midnight and after-midnight pieces gives the whole elapsed time.
Answer: 6 hours 20 minutes

Review

From about 9 PM to about 4 AM is roughly 6 hours, and our exact answer of 6 hr 20 min fits that estimate. The minutes (20) stayed under 60, so no extra hour was carried, which is consistent.

Use 24-hour time (tool 15): 9:55 PM is 21:55 and 4:15 AM next day is 28:15; 28:15 - 21:55 = 6 hr 20 min, matching the split-at-midnight method.

Standards · min grade 3

  • 3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans
💡 When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!
Variant 9 answer: 6 hours 30 minutes

Liam's family boarded a plane at the airport at 7:35 PM on Sunday and arrived at their destination the next day at 2:05 AM (departure-city time). How many hours and minutes long was Liam's family's flight?

Show solution

Understand

A flight left at 7:35 PM Sunday and landed at 2:05 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 7:35 PM to midnight, then from midnight to 2:05 AM.

Givens
  • Departure time: 7:35 PM Sunday
  • Arrival time: 2:05 AM the next day, in departure-city time
  • A full day is 24 hours: 12 hours of AM and 12 hours of PM
Unknowns
  • The flight duration in hours and minutes
Constraints
  • The flight crosses midnight, so the elapsed time spans from PM into the next AM
  • Both clock times are in the same time zone, so no zone adjustment is needed

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

Execute

#7 Identify Subproblems 3.MD.A.1
From 7:35 PM to 12:00 midnight is 4 hr 25 min.
12:00−7:35=4 hr 25 min12{:}00 - 7{:}35 = 4 \text{ hr } 25 \text{ min}
Midnight ends the PM half of the day, so it is the natural splitting point.
#7 Identify Subproblems 3.MD.A.1
From 12:00 midnight to 2:05 AM is simply 2 hr 5 min, since midnight is the start of the AM half.
2:05−12:00=2 hr 5 min2{:}05 - 12{:}00 = 2 \text{ hr } 5 \text{ min}
After midnight the clock reads the AM hours directly, so the second piece is read straight off.
#7 Identify Subproblems 3.MD.A.1
Add the two spans: 4 hr 25 min plus 2 hr 5 min. Minutes: 25 + 5 = 30 min. Hours: 4 + 2 = 6 hr. The total flight time is 6 hr 30 min.
4 hr 25 min+2 hr 5 min=6 hr 30 min4 \text{ hr } 25 \text{ min} + 2 \text{ hr } 5 \text{ min} = 6 \text{ hr } 30 \text{ min}
Adding the before-midnight and after-midnight pieces gives the whole elapsed time.
Answer: 6 hours 30 minutes

Review

From about 7 PM to about 2 AM is roughly 6 hours, and our exact answer of 6 hr 30 min fits that estimate. The minutes (30) stayed under 60, so no extra hour was carried, which is consistent.

Use 24-hour time (tool 15): 7:35 PM is 19:35 and 2:05 AM next day is 26:05; 26:05 - 19:35 = 6 hr 30 min, matching the split-at-midnight method.

Standards · min grade 3

  • 3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans
💡 When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!
Variant 10 answer: 3 hours 45 minutes

Finn's family boarded a plane at the airport at 9:25 PM on Sunday and arrived at their destination the next day at 1:10 AM (departure-city time). How many hours and minutes long was Finn's family's flight?

Show solution

Understand

A flight left at 9:25 PM Sunday and landed at 1:10 AM the next morning (same departure-city time). We find how long the flight lasted by counting the time from 9:25 PM to midnight, then from midnight to 1:10 AM.

Givens
  • Departure time: 9:25 PM Sunday
  • Arrival time: 1:10 AM the next day, in departure-city time
  • A full day is 24 hours: 12 hours of AM and 12 hours of PM
Unknowns
  • The flight duration in hours and minutes
Constraints
  • The flight crosses midnight, so the elapsed time spans from PM into the next AM
  • Both clock times are in the same time zone, so no zone adjustment is needed

Plan

#7 Identify Subproblems · also uses: #1 Draw a Diagram

Because the flight passes midnight, the cleanest approach splits the elapsed time into two easy pieces: from departure to midnight, and from midnight to arrival. A simple time-line sketch keeps the AM/PM crossing clear, then we add the two pieces.

Execute

#7 Identify Subproblems 3.MD.A.1
From 9:25 PM to 12:00 midnight is 2 hr 35 min.
12:00−9:25=2 hr 35 min12{:}00 - 9{:}25 = 2 \text{ hr } 35 \text{ min}
Midnight ends the PM half of the day, so it is the natural splitting point.
#7 Identify Subproblems 3.MD.A.1
From 12:00 midnight to 1:10 AM is simply 1 hr 10 min, since midnight is the start of the AM half.
1:10−12:00=1 hr 10 min1{:}10 - 12{:}00 = 1 \text{ hr } 10 \text{ min}
After midnight the clock reads the AM hours directly, so the second piece is read straight off.
#7 Identify Subproblems 3.MD.A.1
Add the two spans: 2 hr 35 min plus 1 hr 10 min. Minutes: 35 + 10 = 45 min. Hours: 2 + 1 = 3 hr. The total flight time is 3 hr 45 min.
2 hr 35 min+1 hr 10 min=3 hr 45 min2 \text{ hr } 35 \text{ min} + 1 \text{ hr } 10 \text{ min} = 3 \text{ hr } 45 \text{ min}
Adding the before-midnight and after-midnight pieces gives the whole elapsed time.
Answer: 3 hours 45 minutes

Review

From about 9 PM to about 1 AM is roughly 3 hours, and our exact answer of 3 hr 45 min fits that estimate. The minutes (45) stayed under 60, so no extra hour was carried, which is consistent.

Use 24-hour time (tool 15): 9:25 PM is 21:25 and 1:10 AM next day is 25:10; 25:10 - 21:25 = 3 hr 45 min, matching the split-at-midnight method.

Standards · min grade 3

  • 3.MD.A.1 Tell and write time to the nearest minute and solve elapsed time problems — Finding elapsed time across midnight and adding the two spans
💡 When a trip crosses midnight, split the clock at 12:00 into a 'before' and an 'after' piece, then just add them up!