AM and PM make a 24-hour day

3.MD.A.1 · take · grade 3

Archetype: Elapsed Time and Base-Sixty Regrouping · step in a 10-type progression

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: from 9:55 to 10:55 is 1 hour, to 11:55 is 2 hours, and 11:55 to 12:00 is 5 more minutes. That is 2 hr 5 min.

12{:}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 hours and 15 minutes, since midnight is the start of the AM half.

4{:}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 \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 10 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!