Question

Places A and B are 80 km apart from each other on a highway. One car starts from A and another from B at the same time. If they move in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in 1 hour and 20 minutes. Find speed of the cars.

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 8h.

Distance travelled by car I in 8h = 8x km

Distance travelled by car II in 8h = 8y km

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

8x – 8y = 80

⇒ x –y = 10 …(i)

Now, Let two cars meet after 1hr 20 min

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

⇒ 4x + 4y = 240

⇒ x + y = 60 …(ii)

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

x – y + x + y = 10 + 60

⇒ 2x = 70

⇒ x = 35

Putting the value of x = 25 in Eq. (i), we get

35 – y = 10

⇒ y = 25

So, the speed of the two cars are 35km/h and 25 km/hr respectively.