Problem 17 · 2022 Math Kangaroo
Hard
Ratios, Rates & Proportions
work-backwardunit-rate
There are two clocks in my office. One gains one minute every hour; the other loses two minutes every hour. Yesterday I set them both to the correct time. When I checked today, one read 11:00 and the other read 12:00. At what time did I set them yesterday?
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Answer: C — 15:40
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Hint 1 of 2
Each hour the two clocks drift apart by a fixed amount; how fast does the gap between them grow?
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Hint 2 of 2
The clocks now read 60 minutes apart; divide by the hourly drift to find the elapsed time, then step back.
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Approach: use the growing gap between the clocks
- One clock gains 1 min/hour and the other loses 2 min/hour, so they separate by 3 minutes each hour.
- They are now 60 minutes apart (11:00 vs 12:00), which takes 60 / 3 = 20 hours.
- The true time lies between them, and stepping back gives a setting of 15:40, so the answer is C.
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