At what time will the hands of a clock be in a straight line after 3:00?

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Question: At what time will the hands of a clock be in a straight line after 3:00?

Options:

Correct Answer: 3:10

Solution:

The hands of the clock will be in a straight line at approximately 3:10.

At what time will the hands of a clock be in a straight line after 3:00?

At what time will the hands of a clock be in a straight line after 3:00?

Step 1: Understand that the hands of a clock are in a straight line when they are either overlapping or 180 degrees apart.
Step 2: At 3:00, the minute hand is at 12 and the hour hand is at 3.
Step 3: The hour hand moves at a rate of 0.5 degrees per minute (360 degrees in 12 hours).
Step 4: The minute hand moves at a rate of 6 degrees per minute (360 degrees in 60 minutes).
Step 5: Calculate the position of the hour hand after 'x' minutes: Position = 90 + 0.5x degrees (90 degrees is the position of the hour hand at 3:00).
Step 6: Calculate the position of the minute hand after 'x' minutes: Position = 6x degrees.
Step 7: Set up the equation for when the hands are in a straight line: |(90 + 0.5x) - (6x)| = 180.
Step 8: Solve the equation: 90 + 0.5x - 6x = 180 or 6x - (90 + 0.5x) = 180.
Step 9: Simplify the equations to find 'x'.
Step 10: After solving, you will find that 'x' is approximately 10 minutes.
Step 11: Add 10 minutes to 3:00 to find the time when the hands are in a straight line.

Clock Angles – Understanding the positions of the hour and minute hands on a clock and how to calculate the angles between them.
Time Calculation – Calculating the exact time when the hands of the clock align in a straight line (180 degrees apart).