Question

A person pedals from his house to his office at a speed of $x_1$ km/hour and returns by the same route at a speed of $x_2$ km/hour. What is his average speed ?

• A. $\frac{x_1{x}_2}{2x_1-x_2}$
• B. $\frac{x_1{x}_2}{x_1+x_2}$
• C. $\frac{2x_1{x}_2}{x_1+x_2}$
• D. $\frac{x_1{x}_2}{2x_1+x_2}$

Answer 1

Answer: (C)

$\frac{2x_1{x}_2}{x_1+x_2}$

Let the distance from office to home $=y$ km.

Then, the time taken for the round trip $=\frac{y}{x_1}+\frac{y}{x_2}=\frac{y(x_1+x_2)}{x_1{x}_2}$

Total distance travelled in that round trip $=2y$ km

$\therefore Averagespeed=\frac{2y}{\frac{y(x_1+x_2)}{x_1{x}_2}}=\frac{2y{x}_1{x}_2}{y(x_1+x_2)}=\frac{2x_1{x}_2}{x_1+x_2}$.