A watch that gains uniformly, is two minutes slow at noon on Monday and is 4 minutes 48 seconds fast at 2 pm on the following Monday. When was the watch showing the correct time?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2 pm on Wednesday
A watch that gains uniformly gains the same amount in every hour. It starts 2 minutes slow, so it shows the correct time once it has gained back those 2 minutes.
The rate of gain:
Time passed from noon on Monday to 2 pm on the following Monday: 7 days 2 h \(=170\) h
Total gain in that time: from 2 min slow to 4 min 48 s fast, \(2+4\frac{48}{60}=6.8\) min
Gain per hour \(\displaystyle =\frac{6.8}{170}=\frac{1}{25}\) min
When the 2 minutes are made up:
Hours needed to gain 2 min \(=2\times25=50\) h \(=2\) days 2 h
Noon on Monday + 2 days 2 h \(=\) 2 pm on Wednesday