Problem
Broken clock with constant drift
Five clocks each show a time and exactly one is right. The other four are 5 slow, 10 slow, 15 fast and 20 fast. All five readings are the same true time plus these errors. Find the true time.
Reasoning · Grade 2-2 Time and Duration
Your answer
Watch out The middle or the average of the readings looks right, but the errors lean fast, so the average lands at 12:09.
How to solve
Strategy Guess and Check — Since every shown time equals the one true time plus a fixed error, the five shown times must be spaced apart exactly like the five errors -10, -5, 0, +15, +20. List the shown times in order, match the spacing to the errors, then the time aligned with the 0 error is the true time. A quick check confirms it.
1STEP 1
Put the shown times in order
In order the readings run 11:55 through 12:25.
Reading and ordering clock times to the nearest 5 minutes is a Grade 2 skill, and ordering makes the spacing easy to see.
2.MD.C.7Make A Systematic List2STEP 2
Order the errors and compare the spacing
The errors are spaced 5, 5, 15, 5 — the same as the readings.
11{:}55, 12{:}00, 12{:}05, 12{:}20, 12{:}25 → gaps 5,5,15,5
Finding the time between two clock times is elapsed-time reasoning; matching the gap pattern lines up each shown time with its error.
3.MD.A.1Look For A Pattern3STEP 3
Line up each shown time with its error
So they pair in order, and 12:05, the one at zero error, is true.
The clock with no error shows the real time, so the time matched to error 0 is the answer.
3.MD.A.1Guess And CheckMatching the spacing of the shown times to the spacing of the errors pairs each clock with its own error, and the clock paired with error 0 shows the true time.
Why?
Every clock reads the true time shifted by its own error, so the gaps between the readings are exactly the gaps between the errors.
🧱Shift both by the same amount and the difference holdsSlide two points the same distance along the line and the gap between them never changes.
Why?
Because the spacing pattern appears only once, each shown time lines up with exactly one error and no other arrangement fits.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
4STEP 4
Check the match
Applying the four errors to 12:05 reproduces all five readings.
12{:}05-10=11{:}55, 12{:}05-5=12{:}00, 12{:}05=12{:}05, 12{:}05+15=12{:}20, 12{:}05+20=12{:}25
Adding and subtracting minutes to a clock time and getting back exactly the shown set proves the true time is right.
3.MD.A.1Guess And CheckAnswer
12:05
Applying the four errors to 12:05 reproduces all four broken readings (11:55, 12:00, 12:20, 12:25) and the fifth clock shows 12:05 itself, so all five shown times are accounted for with no leftovers. The answer is a real clock time near noon, which fits the picture.
Takeaway
Line up the clock readings in order: their spacing must match the fast/slow amounts, and the one sitting at 'zero error' is the true time. Just Grade 3 time sense!
- Put the shown times in order
- Order the errors and compare the spacing
- Line up each shown time with its error
- Check the match