Problem
Reason about a fast or slow clock
After Hana dropped her clock, it started running fast. She set it to exactly 2:00, and 3 hours later, the clock read 5:09. By how many minutes per hour does Hana's clock run fast?
Measurement & data
Your answer
Watch out Don't assume the clock is slow just because it reads 5:09 — a fast clock shows a time that's ahead of the true time. Subtract the correct time from the displayed time to find how much it gained.
How to solve
Strategy Identify Subproblems — First find the total time the clock gained over 3 hours, then share that time equally across the 3 hours to get the gain per hour.
1STEP 1
Find what a correct clock would show
Three hours after 2:00, a correct clock would read 5:00.
2:00 + 3h = 5:00
Adding the elapsed hours to the start time gives what a correct clock should show — 3 hours after 2:00 is 5:00.
Identify Subproblems3.MD.A.1Time2STEP 2
Find the total extra minutes
5:09 is 9 minutes ahead of the correct 5:00.
5:09 − 5:00 = 9 min
Subtracting the correct time from the displayed time gives the total time the clock has run ahead over the 3 hours.
Identify Subproblems3.MD.A.1Time3STEP 3
Share the extra minutes over each hour
Dividing 9 minutes by 3 hours gives 3 minutes per hour.
9 ÷ 3 = 3 min
The clock gains the same amount every hour, so the 9 minutes is 3 equal hourly shares stacked up. Dividing 9 by 3 undoes that multiplication to find the hourly gain.
Analyze The Units3.MD.A.1TimeDividing the 9 total extra minutes evenly across the 3 hours gives how many extra minutes the clock gains each hour.
Why?
The clock gains time at the same steady rate, so all 3 hours add the same number of extra minutes and the 9-minute total is made of 3 equal shares.
Why?
Three equal hourly shares stacking up to 9 minutes means 9 is three equal groups of one hour's gain, so 9 is 3 times that hourly gain.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Since 9 is 3 times the hourly gain, you recover that hourly gain by undoing the multiplication, which is dividing 9 by 3.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Answer
3 minutes per hour
9 ÷ 3 = 3 min
Check — 3 minutes fast each hour for 3 hours makes 3+3+3=9 minutes, and adding 9 minutes to 5:00 gives 5:09, matching the display.
Takeaway
Subtract the correct time from what the clock shows to get the total gain, then divide by the hours for the gain per hour.
- Correct time → 5:00
- Total gain → 9 minutes
- Gain per hour → 3 minutes
Where next?
Level upsuggested
Another one like thissuggested
Step back and solidifysuggested