Question

Places A and B are 100 km apart on a highway One car starts from A and another from B at the same time at different speeds. If the cars travel in the same direction, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Answer 1

Let the speed of the car which started from the 

place A = x kmph 

and B = y kmph 

Distance travelled by first car in 5h = 5x and in 1h = x 

The distance covered by second car in 5h = 5y and in 1h = y 

By problem when travelled in same direction, 

5x – 5y = 100 ⇒ x – y = 20 …… (1) 

and when travelled towards each other 

x + y = 100 ……. (2) 

Solving (1) and (2),

∴ x = \(\frac{120}{2}\) = 60 

Substituting x = 60 in equation (1) we get 

60 – y = 20 

⇒ y = 60 – 20 = 40 kmph 

Thus the speed of the cars are 60 kmph and 40 kmph.