Question

If a boy walks to his school at a speed of 4km/h, he reaches the school 10 minutes before time. If he walks at 3km/h, he reaches the school 10 minutes late. Find the distance between his house and school.

Answer 1

Let the total time taken by the boy from home to his school be = x hrs
Speed = 4km/h
Also, the distance of his office to home = Speed x time
Speed = 3km/h
Given, Walking at 4km/hr, a boy reaches his school 10 minutes early.

Therefore, time taken by him in reaching the school = `(x - 10/60)"hr"`

And walking at 3km/hr, he will reach 10 minutes late to the school.

Therefore, time taken by him in reaching the school = `(x + 6/60)"hr"`

We, know that distance between the home and school will remain the same

∴ `4(x - 10/60) = 3(x + 10/60)`

⇒ 4(60x - 10) = 3(60x + 10)
⇒ 240x - 40 = 180x + 30
⇒ 60x = 70

⇒ x = `(70)/(60) = (7)/(6)"hr"`

Therefore, the distance between house and school 

= `4(7/6 + 10/60)"km"`

= `4(7/6 + 1/6)"km"`
= 4km.