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
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.