Chapter 1, Problem 43RP

To determine

To calculate: The time at which the hands of clock will form an angle $2\frac{1}{2}$ times as great as the angle formed at $2:00$

Answer to Problem 43RP

The time at which the hands of clock will form an angle $2\frac{1}{2}$ times as great as the angle formed at $2:00$ is $T=2:38:11$

Explanation of Solution

Given information: The initial time of the clock is given to be $2:00$

Formula used: Basic unitary method has been used

Calculation: At $2:00$ , the minutes hands are $10$ minutes apart

So, in order to form an angle $2\frac{1}{2}$ times as great as the angle formed at $2:00$ , the minute hand has to gain

  $(10+25)=35\min$

And, in $60\min$ , minute hand gains $55\min$ of time over the hour hand

Thus, the time needed now is

  $T=\frac{60}{55}(35)\min$ over $2:00$ hours.

Thus, final time after adding the two of these is

  $T=2:38:11$