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If the angle between 2 hands of a clock is 35 degrees and the hour hand is between 3 and 4, what time does the clock show?
The hour hand covers 30 degrees in 1 hour or 0.5 degrees / min
The min hand covers 360 degrees in 1 hour of 6 degrees/ min
Hence, we can say that the the minute hand gains 6 - 0.5 = 5.5 degrees on hour hand, every minute.
At 3 p.m. the angle between the hands was 90 degrees
Hence there can be two possible cases, the minute hand can form a angle of 35 degrees both before and after the it crosses the hour hand.
Let x be the number of minutes past 3.
case 1
90 - 5.5x = 35
x = 10
case 2
5.5x - 90 = 35
x = 125/5.5 = 250/11 = 22 8/11
Hence the angle between hour hand and minute hand will be 35 degrees at 10 and 22 8/11 minutes past 3
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