Given Data

1. Time interval: Between 4 o'clock and 5 o'clock.

Question

At what exact time between 4 and 5 o'clock will the hands of a clock coincide?

Answer

21 9/11 minutes past 4.

Solution

1. At 4 o'clock, the hour hand is at 20 minute spaces (120 degrees) ahead of the minute hand.
2. For the hands to coincide, the minute hand must gain 120 degrees on the hour hand.
3. Relative speed of the minute hand = 5.5 degrees per minute (11/2 degrees/min).
4. Time required = 120 / (11 / 2) = 240 / 11 minutes = 21 9/11 minutes.
5. Therefore, the hands coincide at 21 9/11 minutes past 4.