At what time between 2:00 and 3:00 do the hands of the clock overlap?

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Question: At what time between 2:00 and 3:00 do the hands of the clock overlap?

Options:

Correct Answer: 2:15

Solution:

The hands overlap at approximately 2:10 and 10/11 minutes.

At what time between 2:00 and 3:00 do the hands of the clock overlap?

At what time between 2:00 and 3:00 do the hands of the clock overlap?

Step 1: Understand that the hour hand and minute hand of a clock move at different speeds.
Step 2: The hour hand moves at 0.5 degrees per minute (360 degrees in 12 hours).
Step 3: The minute hand moves at 6 degrees per minute (360 degrees in 60 minutes).
Step 4: At 2:00, the hour hand is at 60 degrees (2 hours x 30 degrees per hour).
Step 5: Let 'm' be the number of minutes after 2:00 when the hands overlap.
Step 6: The position of the hour hand after 'm' minutes is: 60 + 0.5m degrees.
Step 7: The position of the minute hand after 'm' minutes is: 6m degrees.
Step 8: Set the two positions equal to find when they overlap: 60 + 0.5m = 6m.
Step 9: Rearrange the equation: 60 = 6m - 0.5m, which simplifies to 60 = 5.5m.
Step 10: Solve for 'm': m = 60 / 5.5, which is approximately 10.909 minutes.
Step 11: Convert 10.909 minutes to minutes and seconds: 10 minutes and 54.54 seconds.
Step 12: Therefore, the hands overlap at approximately 2:10 and 10/11 minutes.

Clock Angles – Understanding the movement of clock hands and how to calculate the angles between them.
Time Calculation – Calculating the exact time when the minute and hour hands coincide.