At what time between 4 pm and 5 pm will  the hour hand and the minute hand of a clock coincide?

To find out when the hour and minute hands coincide between 4 pm and 5 pm, we need to understand that the minute hand moves 12 times faster than the hour hand.

1. At 4 pm, the hour hand is at 4 on the clock and the minute hand is at 12.

2. The minute hand will have to make a little more than one full revolution to catch up with the hour hand.

3. The minute hand moves 12 times faster than the hour hand, so it will take a little more than 1/12th of an hour (or 5 minutes) to catch up.

4. However, in that time, the hour hand will also have moved a little.

5. To find the exact time, we can set up the equation: 12*(4 + m/60) = m, where m is the number of minutes past 4 o’clock.

6. Solving this equation gives m = 120/11 minutes, or approximately 10.91 minutes.

7. Therefore, the hour and minute hands will coincide at approximately 4:11 pm.