Question

91. Places A and B are 100 km apart on a highway. One car starts from A
and another from B at the same time. If the cars travel in the same direction at
different speeds, they meet in 5 hours. If they travel towards each other, they
meet in 1 hr. What are the speeds of the two cars?
[CBSE 2009] ​

Answer 1

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Answer 2

Answer:

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time.

Let us assume that the speed of the car from place A and B are

a

and

b

km/hr.

Case 1: The cars travel in the same direction at different speeds, they meet in 5 hours. The effective speed is the difference between the speed of two cars.

Speed=Distance / Time

a−b=100 / 5

a−b=20

Case 2: If they travel towards each other, they meet in 1 hour. The effective speed is the sum of the speed of two cars.

Speed=Distance / Time

a+b=100 / 1

a+b=100

Adding the two equations of speed:

(a+b=100)+(a−b=20)

2a=120

a=60

Since

a−b=20b=40

The speed of two cars are

60kmph and 40kmph.

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