Chapter 9.5, Problem 23P

To determine

To find: The speed of the car.

Answer to Problem 23P

The speed of the while going to the destination was 80 km/hand while returning its speed was 40km/h.

Explanation of Solution

Given information:

Total distance = 120 km.

Total time taken = 4 hour 30 minutes.

Calculation:

Let, the speed of the while going to the destination was $x$ km/h and while returning its speed was $\frac{x}{2}$ km/h.

4hour 30 minutes = $4\frac{1}{2}\text{hr}=\frac{9}{2}\text{hr}$

By question

  $\begin{array}{c}\frac{120}{x}+\frac{120}{\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\frac{9}{2}\\ \frac{120}{x}+\frac{240}{x}=\frac{9}{2}\\ \frac{360}{x}=\frac{9}{2}\\ 9x=360\times 2\end{array}$

  $\begin{array}{c}x=\frac{360\times 2}{9}\\ x=80\end{array}$

Therefore,

  $\begin{array}{c}\frac{x}{2}=\frac{80}{2}\\ =40\end{array}$

Therefore, the speed of the while going to the destination was 80 km/h and while returning its speed was 40km/h.