Question

A boy goes from his house to his friend's house with speed u. Finding his friend's house door closed, he returns back to his own house with speed v. Then the average speed of the boy is

• A. $\frac{u+v}{2}$
• B. $\frac{2uv}{u+v}$
• C. $\sqrt{uv}$
• D. $zero$

Answer 1

The correct option is B

$\frac{2uv}{u+v}$

Step 1: Assumptions

Now, let s be the distance between the boy and his friend's house, t₁ be the time taken to reach his friend's house, t₂ be the time taken to return and t be the total time taken.

u is the speed while reaching his friend's house and v the speed while returning.

Step 2: Formula used

We know that;

The average speed of a body is given by $\frac{Totaldis\tan cetravelled}{Totaltimetaken}$

So we have,

$$\begin{gathered} t_1=\frac{s}{u} \\ {t}_2=\frac{s}{v} \end{gathered}$$

Therefore,

$t=t_1+t_2=\frac{s}{u}+\frac{s}{v}$

Now,

Total distance traveled = 2s

Total time taken = $\frac{s}{u}+\frac{s}{v}$

Strep 3:Finding average speed:

$$\begin{gathered} \mathrm{Average}\mathrm{speed}=\frac{2s}{\frac{s}{u}+\frac{s}{v}} \\ =\frac{2suv}{s(u+v)} \\ =\frac{2uv}{(u+v)} \end{gathered}$$

Therefore, the correct option is (B).