Two cars start together from the same place in the same direction.
Question:

Two cars start together from the same place in the same direction. The first go with a uniform speed of 60 km/hr. The second goes at a speed of 48 km/hr in the first hour and increases the speed by 1 km each succeeding hour. After how many hours will the second car overtake the first car if both cars go non – stop

Solution:

Given :

Two cars start together from the same place and move in the same direction.

The first car moves with a uniform speed of 60km/hr.

The second car moves with 48km/hr in the first hour and increases the speed by 1 km each succeeding hour.

Let the cars meet at n hours.

Distance travelled the first car in n hours = 60×n

Distance travelled by the second car in n hours is

$=\frac{n}{2}\{2 \times 48+(n-1) \times 1\}$

Tip: –

When the cars meet the distances travelled by cars are equal.

$\frac{\mathrm{n}}{2}\{2 \times 48+(\mathrm{n}-1) \times 1\}=60 \times \mathrm{n}$

$96+(n-1)=120$

n = 25

∴ The two cars meet after 25 hours from their start and overtake the first car.