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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 the two cars?

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Solution

Let the speed of car which starts from A be x and from B be y Therefore,speed of car from A in 5 hours = 5 x speed of car from B in 5 hours = 5 y Case 1 Both the cars travel in the same direction, Therefore, 5 x - 5 y = 100 5 (x - y) = 100 Thus , x -y = 100/5= 20 Also, x = 20 + y . . . . . . . . (1) Case 2 Both the cars travel towards each other, Therefore, x + y = 100 From (1) , {20 + y} + y = 100 20 + 2 y = 100 2 y = 100 - 20 2 y = 80 Thus, y = 80/2 = 40 Km/hr Substituting y = 40 in (1), x = 20 + y = 20 + 40 = 60 Km/hr Thus, the speed of car which starts from A is 60 Km/hr and that of the car which starts from B is 40 Km/hr

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