It would be better to have one hand

Geometry Level 3

In $24$ hours, how many times does the minute hand cross exactly over the hour hand of a clock? Hence find the time in hours in which the minute hand cross over hour hand after the previous crossing.

24, 1\frac{1}{11}

22, 1\frac{1}{11}

22, 1\frac{1}{13}

22, 1\frac{1}{59}

24, 1\frac{1}{59}

1 solution

Rohit Sachdeva
Apr 19, 2015

First part is easy to find out. One time each hour, the minute hand crosses over hour hand, except first 12AM & last 12AM (say we start counting from 12AM). Hence, 22 times.

Now each hour, the hour hand moves forward by 30°. To cover this 30° the minute hand will take 30/(11/2)mins or 60/11mins or 1/11hr. Apart from this, the minute hour has to anyways cover 1hr. So in total 1+1/11hr.

Note: relative speed of minute hand over hour hand is (11/2)° per minute

You could also approach the second part as follows: It crosses $22 times$ in $24 hours$ , or, it cross $1 time$ in $\frac{24}{22}\times 1 hours$ i.e. $\frac{12}{11} hours$

Manish Mayank - 6 years, 1 month ago

It would be better to have one hand

1 solution

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