A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day?(Find the nearest true time)1 PM12.30pm12.48pm1.30pm
Question
A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day?(Find the nearest true time)1 PM12.30pm12.48pm1.30pm
Solution
The clock gains 10 minutes in 24 hours. This means that when the clock reads 24 hours and 10 minutes (or 1,450 minutes), the actual time passed is 24 hours (or 1,440 minutes).
The clock reads 1 p.m. the following day, which is 29 hours after it was set at 8 a.m. the previous day. This is 1,740 minutes.
To find the actual time passed, we can set up a proportion:
10 minutes gain / 1,450 minutes = X minutes gain / 1,740 minutes
Solving for X gives us X = (10/1450) * 1740 = 12 minutes
So, the actual time is 12 minutes less than the time the clock reads. Therefore, the true time when the clock indicates 1 p.m. on the following day is 12:48 p.m.
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