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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. 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 hour.What are the speeds of two cars?


Solution

Let the speeds of the cars be x km/hr and y km/hr
Case 1:
When the cars are going in the same direction
Relative speed = x - y
Distance = 100 km
Time = 100 / (x - y) = 5 hrs
x - y = 100 / 5=20
x – y = 20 ------------- (1)

Case 2:
When the cars are going in the opposite direction
Relative speed = x + y
Time =100 / (x + y) = 1 hrs
x + y = 100 ------------- (2)

Solving the equations (1) and (2),
x = 60
y = 40
Hence the speeds of the cars are 60 km/hr and 40 km/hr.


Mathematics
RD Sharma
Standard X

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