A medium question on clocks and time for P3–P4, with a step-by-step solution, diagrams and the answer. Every year of the Hua Xia Cup has clock questions, from time passed in P1 to the angle between the hands in P6.
The question
May's alarm clock loses 1 minute every hour.
One day at 6:00 am she sets it to the right time.
Later that day she sees it showing 2:51 pm.
What is the real time then? (It is exactly on the hour in the afternoon: for 3 pm, answer 3.)
Show the hints (2)
💡Hint 1: In each real hour, how many minutes does the alarm clock move on?
💡Hint 2: From 6:00 am to 2:51 pm, how many minutes has the alarm clock moved on altogether?
Worked solution
Have a go first, then read the solution step by step.
1.In each real hour the clock moves on 60 − 1 = 59 minutes.
2.From 6:00 am to 2:51 pm the clock has moved on 8 hours 51 minutes, which is 531 minutes.
3.531 ÷ 59 = 9, so 9 real hours have passed.
4.9 hours after 6:00 am is 3:00 pm, so the answer is 3.
⚠️Common mistake: taking the clock's 2:51 pm as the real time, or thinking the clock is only 1 minute out. The error builds up every hour.
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