Problem
Reason about a fast or slow clock
Hana set her clock to exactly 2:00. After 3 real hours it read 5:09 instead of 5:00, because it runs fast. Find how many minutes per hour the clock gains.
Measurement & data
Your answer
Watch out The question asks for the gain in a single hour, not the total minutes gained over the whole 3 hours.
How to solve
Strategy Identify Subproblems — First find the total extra time the clock gained over the whole 3 hours (subproblem 1), then share that extra time equally across the 3 hours to get the gain per hour (subproblem 2).
1STEP 1
Find what a correct clock would show
Three hours after 2:00, a correct clock would read 5:00.
2{:}00 + 3 hours = 5{:}00
Adding 3 hours to the hour shows where a good clock should be.
3.MD.A.1Identify Subproblems2STEP 2
Find the total extra minutes
Hana's clock shows 5:09 but should show 5:00, so it has gained 9 minutes over the 3 hours.
5{:}09 - 5{:}00 = 9 minutes
The difference between the displayed time and the true time is the total time the clock ran ahead.
3.MD.A.1Identify Subproblems3STEP 3
Share the extra over each hour
The 9 extra minutes were gained evenly across 3 hours, so divide 9 by 3.
9 ÷ 3 = 3
Splitting the total gain equally among the hours gives the gain in each single hour.
3.MD.A.1Analyze The UnitsDividing 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
Check by building up: 3 minutes fast each hour for 3 hours is 3 + 3 + 3 = 9 minutes, so the clock shows 5:00 + 9 min = 5:09, matching the figure.
Takeaway
Find the total minutes the clock got ahead, then split it across the hours: just Grade 3 time-and-dividing!
- Find what a correct clock would show
- Find the total extra minutes
- Share the extra over each hour
Where next?
Level upsuggested
Another one like thissuggested
Step back and solidifysuggested