At how many minutes after noon do the hour hand and minute hand of an analog clock first meet again? Explain your answer to the nearest whole number.
Using basic knowledge of a clock I got 65. Is there also an algebraic equation that can be set up to answer this question?
The explanation is as follows: At noon both the hour hand and the minute hand are at 12. As the minute hand starts moving, so does the hour hand, although at a much slower pace. After 60 minutes, the minute hand would once again be on 12 and the hour hand would now be on 1. After 5 more minutes , the minute hand will meet the hour hand once again - at this time right after 1.
Writing the above I realized that the hour hand moves at 1/12 of the speed of the minute hand. Still not sure how to use it to set up the equation.
Using basic knowledge of a clock I got 65. Is there also an algebraic equation that can be set up to answer this question?
The explanation is as follows: At noon both the hour hand and the minute hand are at 12. As the minute hand starts moving, so does the hour hand, although at a much slower pace. After 60 minutes, the minute hand would once again be on 12 and the hour hand would now be on 1. After 5 more minutes , the minute hand will meet the hour hand once again - at this time right after 1.
Writing the above I realized that the hour hand moves at 1/12 of the speed of the minute hand. Still not sure how to use it to set up the equation.