Chapter 1.3, Problem 17PSC

To determine

To find : The first time after 12:00, when minute hand and hour hand together.

Answer to Problem 17PSC

1:05 am

Explanation of Solution

Given information :

The first time when both hour hand and minute hands overlapping each other was 12:00

Concept used :

  $1°=6^{\prime }$

Calculation:

Here, we have

For $n$ hours, the minute hand completes $n$ complete round.. For the same duration , the hour hand completes $\frac{n}{12}$ round..

Firstly, both the minute and hour hands overlap, the minute hand would have completed one more than the hour hand. So we have $n=\frac{n}{12}+1$ . This infers that the first overlap happens after $n=\frac{n}{12}+1=\frac{12}{11}\text{hours}\sim \text{1:05}\text{am}$ .