Question

By how many degrees does the hour hand lag behind the minute hand in a span of 42 minutes, if initially they are at the same position?

Answer 1

$\bold{231^{\circ}}$ the hour hand lag behind the minute hand in a span of 42 minutes.

Given:

The hour hand and the minute hand are at the same position initially, later 42 minutes passed.

To find:

How many degrees does the hour hand lag behind the minute hand?

Solution:

We know that the hours hand completes 360° in 12 hours, that is $12\times60$minutes.

Then, the angular speed of the hours hand in min is$\frac{360}{12} \times 60=\frac{1}{2}$ degree per minute.

The minutes hand completes $360^{\circ}$ in a span of 1 hour, that is in 60 minutes.

Then, the angular speed of the minutes hand in min is $\frac{360}{60}$ = 6 degree per minute.

So, in 1 minute, the minutes hand gains$\left(6-\frac{1}{2}\right)$ degrees over the hours hand.

Therefore, in 42 minutes, the minutes hand gains $42 \times\left(6-\frac{1}{2}\right)$degrees per minute

$\begin{array}{l}{=42 \times \frac{11}{2}} \\ {=231^{\circ}}\end{array}$

$231^{\circ}$ the hour hand lag behind the minute hand in a span of 42 minutes.