Question

Two towns, A and B, are 120 km apart on the highway. One car starts from A and the other from B at the same time, at different speeds. If the cars travel in the same direction, the cars meet in 4 hours. But when they travel towards each other, they meet in 1 hour. Find their speeds.

Answer 1

Here, 

Let the Speed of the first car = x km/h,

And the Speed of the second car = y km/h,

According to the given condition,

(i) When travelling in the same direction:

Relative speed = difference in speeds = x − y

Time taken = 4 hours

Distance covered relative to each other = 120 km

(x − y) × 4 = 120

x − y = `120/4`

x − y = 30     ...(1)

(ii) When travelling towards each other:

Relative speed = sum of speeds = x + y

Time taken = 1 hour

Distance covered = 120 km

(x + y) × 1 = 120

x + y = 120     ...(2)

Now, adding equation (2) and equation (1):

(x + y) + (x − y) = 120 + 30

x + y + x − y = 150

2x = 150

x = `150/2`

∴ x = 75

Substitute x = 75 in equation (2):

75 + y = 120

y = 120 − 75

∴ y = 45

Hence, the Speed of the first car is 75 km/h, and the Speed of the second car is 45 km/h.