Question

A man went to market at a speed of 4 km/h and returned at a speed of 3km/h. If he took 30 minutes more in returning, find the distance of the market from his home.

Answer 1

Let the distance of the market from his home = x km.
Speed = 4 km/h

Time taken = ${\displaystyle \frac{x}{4}\text{hrs}}$

Also, distance of the market to home = x km.
Speed = 3 km/h

Time taken = ${\displaystyle \frac{x}{3}\text{hrs}}$

As per the condition, he took 30 minutes more in returning from the market.

${\displaystyle \frac{x}{3}-\frac{x}{4}=\frac{30}{60}}$

⇒ ${\displaystyle \frac{4x-3x}{12}=\frac{1}{2}}$

⇒ ${\displaystyle \frac{x}{12}=\frac{1}{2}}$
⇒ x = 6km.