Question

A student walks to school at the rate of 7.5 km/hr and reaches 10 minutes late. If he walks at the speed of 10 km/hr he is 10 minutes early. What is the distance to the school in km?

• A. 10

Answer 1

The correct option is A 10
Let the distance to the school be 1 km, then the time taken to cover 1 km at the rate of 7.5 km/hr is $\frac{\text{Distance}}{\text{Speed}}=\frac{1}{\frac{15}{2}}\text{hr}=\frac{2}{15}\times 60\text{min}=8\text{min}$

Time taken to cover 1 km at the rate of 10 km/hr $=\frac{\text{Distance}}{\text{Speed}}=\frac{1}{10}hr=\frac{1}{10}\times 60min=6min$

Difference in time taken = ( 8 - 6 ) = 2 min.

When the difference in time is 2 min, the distance is 1 km.

The student reaches 10 min late with 7.5 km/hr and 10 min early with 10 km/hr, so the time difference is 20 min.

For the time difference of 20 min, the distance is $\frac{20}{2}=10\text{km}$