Question

A person walks from his house to his office at a speed of x1km/h and return by the same route at a speed of x2km/h.his average speed is.

Answer 1

Given

• Goes at speed of x1 km/hr
• Returns at speed of x2 km/hr

To Find

• His Average Speed?

Solution:

Let the distance between the house and office be Y km

Time taken to go Office = ${\tt{ \dfrac{Y}{x_1} }}$ hour

again,

Time Taken to come Back to home = ${\tt{ \dfrac{Y}{x_2} }}$ hour

Total time taken =

${\tt{ \dfrac{Y}{x_1} + \dfrac{Y}{x_2} }} \\ \\ \\ \implies{\tt{ \left( \dfrac{x_1 + x_2}{x_1x_2} \right) Y }}$

Total distance travelled by the person = Y + Y

= 2Y km

$\\ \colon\implies{\tt{ Average \ Speed = \dfrac{2 \cancel{Y} }{ \left( \dfrac{x_1+x_2}{x_1x_2} \right) \cancel{Y} } }} \\ \\ \\ \colon\implies{\tt{ \dfrac{2}{ \left( \dfrac{x_1+x_2}{x_1x_2} \right) } }} \\ \\ \\ \colon\implies{\tt{ \left( \dfrac{2x_1x_2}{x1+x_2} \right) }}$

Hence,

• The Average Speed of Person is ${\boxed{\tt{ \dfrac{2x_1x_2}{x1+x_2} }}}$ .