The Fast and Furious Clock

Algebra Level 3

Arpan has the misfortune to own an unreliable clock. This one speeds up by exactly 15 minutes every hour. It is now showing 03:00 a.m. and Arpan knows that it was correct at midnight, when he set it. The clock stopped four hours ago, what is the correct time? How to answer - If the time is 10 : 40 a.m. , then give the answer as 10 + 40/60 = 10 + 0.67 = 10.67.


The answer is 6.4.

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1 solution

Arpan Sarangi
Jul 18, 2015

Since the clock is gaining 15 minutes every hour, for every real hour that has passed, the clock will show 75 minutes.

Since the clock shows 3:00 am, we know that 180 clock minutes have passed.

This equals 144 real minutes (180 / 75 x 60), so the clock shows 2:24 am.

The clock stopped 240 minutes ago (4 hours), so the time must now be 6:24 am. So, the required answer is 6 + 24/60 = 6 + 0.4 = 6.4.

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