A certain slow clock loses 15 minutes every hour. Suppose the clock is set to the correct time at 9 AM.....?

Question

A certain slow clock loses 15 minutes every hour. Suppose the clock is set to the correct time at 9 AM. What will the correct time be when the slow clock first shows 10 AM? Please explain me, don't just post the answer. Why isn't it 9:45?

Thank you!!!!

Answer 1

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If the slow clock loses 15 mins every hour, then that means after 60 mins, it shows 45 mins have elapsed.

45 / 60 = 3 / 4

So the slow clock runs at 3/4 the rate it should.

Therefore if the slow clock shows an elapsed time of 60 mins, we can calculate the real elapsed time R, as:

R * 3 / 4 = 60

R * 3 = 60 * 4

R = 60 * 4 / 3

R = 80 mins

So if the slow clock was correct at 9 AM, and it's now showing 10 AM, the real time is 10:20 AM.