Question

If a motorcyclist drives at the rate of 24km/h, he reaches his destination 5 minutes too late. If he drives at the rate of 30 km/h, he reaches his destination 4minutes too soon. How far is his destination?

Answer 1

Let the total taken by the motorcyclist to reach his destination = x hrs
Speed = 24km/h
Also, the distance of his destination from the start = Speed x time
Speed = 30km/h
Given, driving at 24km/hr, a person reaches his destination 5 minutes late.

Therefore, time taken by him in reaching the destination = `(x + 5/60)"hr"`

And driving at 24km/hr, he will reach 4 minutes early to the destination.

Therefore, time taken by him in reaching the destination = `(x - 4/60)"hr"`

We, know that distance between the start and destination will remain the same

∴ `24(x + 5/60) = 30(x - 4/60)`

⇒ 24(60x + 5) = 30(60x - 4)
⇒ 1440x + 120 = 1800x - 120
⇒ 360x = 240

⇒ x = `(240)/(360) = (2)/(3)`

Therefore, the distance of his destination

= `30(2/3 - 4/60)"km"`

= `30((40 - 4)/60)`
= 18km.