Question

If the minute hand and the hour hand of the clock are currently between 3 and 4, then how much again?
Will they come on top of each other in minutes?​

Answer 1

Answer:

$\sf{Given}$

The minute hand and the hour hand of the clock are currently between 3 and 4.

To find:

How long will it take to come on top of each other.

Solution:

According to the given condition, it's 17.5 minutes passed to 3 o'clock in the clock.

At 4 o'clock, the minute hand will be on 12 and hour hand will be on 4.

Note:

For each minute hour hand moves half degree.

There is angle of 30⁰ between any two numbers on the clock.

Now, For minute hand to go to 4 it will take 20 minutes, till that hour hand will make angle of 10⁰ with the minute hand.

Note:- Minute hand will make angle of 6⁰ with 4 for each minute and hour hand will make angle of 3⁰ more for each minute.

For both being on top of each other, Angle made by minute hand should be same as angle made by hour hand with 4.

Let required time be n minutes

Hence, 6n = 10 + 3n

Therefore, n ≈ 3.3 minutes

Hence, time in clock will be 23.3 minutes passed to 4 o'clock.

Time required can be given by subtracting 17.5 minutes passed to 3 o'clock from 23.3 minutes passed to 4 o'clock.

i.e. Time required is 1 hr 5.8 minutes

In minutes it is 65.8 minutes.