Two clocks with ordinary 12-hour dials (no a.m./p.m. shown) are set right at 12 noon. One gains 1 minute every hour and the other loses 1 minute every hour. After how many days will the two dials next show the same time?

Explanation

1. 01

   The clocks drift apart by $1 + 1 = 2$ minutes every hour.

2. 02

   On a 12-hour dial they show the same time again when the gap is 12 hours $= 720$ minutes.

3. 03

   Time $= 720 \div 2 = 360$ hours $= 360 \div 24 = 15$ days.