Question

If the minute hand of a clock is 20 degrees behind the hour hand at this moment, then in 18 minutes, the minute hand will be how many degrees ahead of the hour hand?

Answer 1

There are 60 min on clock, this also represents 360 degrees
---> 1 min = 6 degrees or 1 degree = 10 sec

20 degrees = 20*10 = 200 sec = 3 min 20 sec
Go forward 18 min
---> 18 - 3.33 = 14.66 = 14 min 40 sec = 880 sec = 88 degrees

So now you are 88 degrees ahead of hour hand, assuming the hour hand has not moved.
However, it moves slowly around the circle, There are 12 hours or 720 min for hour hand
----> 1 min = 0.5 degrees or 1 degree = 2 min
Going Forward 18 min, the hour hand has moved 9 degrees
Subtract this from the 88 degrees found above because hour hand is getting closer to minute hand
---> 88 - 9 = 79

Answer is 79 degrees

Answer 2

In short, 18 minutes, the minute hand advances by 18 * 6 = 108 deg. (As, Each minute on a clock face corresponds to an angle of 360/60 = 6 deg.)

The hour hand advances at 1/12 of the rate of the minute hand, so,
18 minutes it advances by 108/12 = 9 deg.

In 18 minutes, the minute hand is ahead of the hour hand by 20 degrees
(108 - 9 - 20) = 79 deg.

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