Question

A car travels a certain distance with a speed of 40 m/s and returns with a speed of u. If the average speed of the whole journey is 48 m/s, what is the value of u?

Answer 1

Step 1: Given data

A car travels a certain distance with a speed of 40 m/s.

Returning speed is ‘u’ m/s.

The average speed of the car is 48 m/s.

Let, x is the certain distance traveled by car and t be the total time of the whole journey.

Step 2: Finding the value of u

We know that;

$$\begin{gathered} \mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}} \\ \mathrm{Average}\mathrm{speed}=\frac{\mathrm{Total}\mathrm{distance}}{\mathrm{Total}\mathrm{time}}. \end{gathered}$$

So, total time $t=\left(\frac{x}{40}+\frac{x}{u}\right)$

And average speed is given by,

$V_a=\frac{2x}{{\displaystyle \frac{x}{40}}+{\displaystyle \frac{x}{u}}}=\frac{40u\times 2x}{x\left(40+u\right)}=\frac{80u}{40+u}.$

According to the question;

$$\begin{gathered} V_a=\frac{80u}{40+u}=48 \\ 1920+48u=80u \\ 32u=1920 \\ u=\frac{1920}{32}=60 \\ u=60m/s. \end{gathered}$$

Hence, the value of u is 60 m/s.