A watch gains 5 seconds in 3 minutes and was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4, the true time is:

3:59 7/12 p.m.
4 p.m.
3:58 7/11 p.m.
4:02 3/11 p.m.

Correct answer: 4 p.m.

Solution

The watch gains 5 seconds in 180 seconds, so in 185 seconds of watch time, only 180 seconds of true time pass. Thus, true time = watch time × 180/185 = watch time × 36/37. From 7 a.m. to 4:15 p.m., the watch shows 9 hours 15 minutes = 555 minutes, so true elapsed time is 555 × 36/37 = 540 minutes = 9 hours. Therefore, the true time is 4 p.m.

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