Chapter 1, Problem 41RP

To determine

To Calculate: The next time after 3:00 at which the hands of the clock will form an ${90}^0$ angle is to be calculated

Answer to Problem 41RP

The time in nearest seconds when the hands of the clock will form a ${90}^0$ angle is $T=3:32:44$

Explanation of Solution

Given information: We are given that the hands of the clock form an angle of ${90}^0$ at 3:00

Formula used: The two hands of the clock will be at right angles between H and $(H+1)$ o Clock at

  $T=(5H\pm 15)\frac{12}{11}$ minutes

Calculation: Thus, using the above formula we can say that

  $T=(5(3)\pm 15)\frac{12}{11}\min =0\min ,\frac{360}{11}\min$

Removing the first answer, we get our final answer as

  $T=3hr+\frac{360}{11}\min$

Converting it to the nearest seconds, we get

  $T=3:32:44$ sec