Question

Sahil rides his bicycle at the speed of 15km/h and reaches school late by 2 minutes. On increasing the speed by 5km/ h , he reaches 8 minutes early. Find the distance between the school and his house.

Answer 1

Let the distance between his school and home be x km.
Then, the time taken by him to reach the school when his speed is 15 km/h
$=\frac{x}{15}hours=60\times \frac{x}{15}minutes=4xminutes$
$(Times=\frac{distance}{speed}and1hour=60minutes)$
The time taken by him to reach the school when his speed increases by 5 km/h i.e. at speed of 20 km/h
$=\frac{x}{20}hours=60\times \frac{x}{20}minutes=3xminutes$
According to the question, at speed of 15 km/h Sahil reaches school late by 2 minutes; and at speed of 20 km/h
he reaches school 8 minutes early. So, there is a difference of 10 minutes between the times taken at speed of 15 km/h and at speed
of 20 km/h. Therefore we can write
$4x-3x=10$
$\Rightarrow x=10$
Hence the distance between his home and school is 10 km.