A boy goes to a cycle shop by walk at ` 5 km h^(-1)` and comes back home by cycle at a speed of ` 15 km h^(-1)` , find out the average speed of the boy.

Explanation

Speed = `("distance")/("time")`
Time = `("distance")/("speed")`
Take the distance as x.
Time taken to reach the cycle shop `t_(1)=x/5`.
Time taken to return `t_(2)=x/15`
Average speed = `("total distance")/("total time")=(x+x)/(t_(1)+t_(2))`
= `(2x)/(x/5+x/15)=(2x)/((3x+x)/15)`
= `(15xx2x)/(4x)=30/4=7.5kmh^(-1)`