Two clocks are set right at 9 a.m. The first gains 2 minutes every hour and the second loses 3 minutes every hour. When the first clock shows 3:12 p.m., what does the second clock show?

Explanation

1. 01

   First find the true time. The first clock shows 62 minutes for every 60 true minutes.

2. 02

   It has shown 6 h 12 min $= 372$ minutes, so true time passed $= 372 \times \frac{60}{62} = 360$ minutes: it is 3:00 p.m.

3. 03

   The second clock has lost $6 \times 3 = 18$ minutes, so it shows 2:42 p.m.