Question

Two places A and B are 120 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 6 hours, and if they move in opposite directions, they meet in 1 hour 12 minutes. Find the speed of each car.

Answer 1

Let the speed of car I = x km/hr

And the speed of car II = y km/hr

Car I starts from point A and Car II starts from point B.

Let two cars meet at C after 6h.

Distance travelled by car I in 6h = 6x km

Distance travelled by car II in 6h = 6y km

Since, they are travelling in same direction, sign should be negative

6x – 6y = 120

⇒ x –y = 20 …(i)

Now, Let two cars meet after 1hr 12min

Since they are travelling in opposite directions, sign should be positive.

⇒ 6x + 6y = 120 × 5

⇒ x + y = 100 …(ii)

On adding (i) and (ii) , we get

x – y + x + y = 20 + 100

⇒ 2x = 120

⇒ x = 60

Putting the value of x = 60 in Eq. (i), we get

60 – y = 20

⇒ y = 40

So, the speed of the two cars are 60km/h and 40 km/hr respectively.