Clocks

Algebra Level 4

Your friend wanted to give you something nice for your birthday, but he is not very bright, so he gave you a clock that gains twelve minutes every hour. Still, you promised him you would use it, so you set the clock correctly at midnight and go about your day. At the end of the day, the clock reads 10 pm. If it stopped exactly four hours ago, what time is it?

[Express your answer as a single four digit number. For example, if your answer was 11:59, you would type 1159]

The answer is 1020.

2 solutions

Daniel Oh
May 25, 2015

Every 72 minutes on the clock, one real hour passes by. The clock stopped at 10 pm, 22 fake hours from midnight.

So,

22*60=1320

1320/72=18 1/3

18 1/3 hours from midnight is 6:20. Since the clock stopped 4 hours ago, it is currently 10:20.

Really nice problem!

Ashwin Padaki - 6 years ago

Noel Lo
Jun 2, 2015

For every 60 minutes passes, the clock shows a time that has advanced by 60+12 = 72 mins. So the actual amount of time passed is $\frac{60}{72} = \frac{5}{6}$ of that depicted by the clock. When the clock has shown that 22 hours $= 22 \times 60= 1320$ mins have passed, in reality, $1320 \times \frac{5}{6} = 1100$ mins have passed. 1100 mins = 18 hrs 20 mins so the clock stopped at $6.20$ pm. Four hrs from then on = $10.20$ pm so required answer = $\boxed{1020}$ .

Clocks

The answer is 1020.

2 solutions

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