### Brain Teasers

# Time gain !!!

A watch which gains 5 seconds every 3 minutes was set correctly at 7 a.m. In the afternoon of the same day, when the watch indicated a quarter past 4 o'clock, what was the true time?

### Answer

The true time is 4 p.m.The watch advanced 9 hours and 15 minutes (555 minutes) between 7 am and 4:15 pm.

For every 3 minutes and 5 seconds (185 seconds) that the watch advances, actual time progresses 3 minutes (180 seconds).

Therefore you need to figure out how many 185-second intervals there are in 555 minutes and then figure out how much actual time passes in the same number of 180-second intervals.

Number of 185-second intervals in 555 minutes:

(555 minutes * 60 seconds/minute)/185 seconds = 180 intervals

Amount of time passing in 180, 180-second intervals:

180 intervals * 180 seconds / (60 seconds/minute) = 540 minutes

Therefore, in the time that the watch advanced 555 minutes, actual time advanced 540 minutes. The difference is 15 minutes, making the actual time 4:00 pm.

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## Comments

This is even more complicated than the meter teaser. Very good and really hard.

I liked the teaser but there is a flaw in the answer. From 7 am to 4:15 pm there is 9hrs and 15 min = 9x60+15=540+15=955 minutes not 965. An easy way to look at it is that each hour 100 seconds are gained. After 9 hours 900 seconds or 15 minutes have been gained so at 40 O'clock real time, the watch will show 4:15!

I also get 40 PM. The idea is correct, but the initial claim of 565 minutes throws off the remaining calculations.

I used the same method as jimbo; the one given in the answer is much more complicated than necessary.

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