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# Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:(iv) 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? Q.4(4)

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How i solve the question of class 10th math of Pair of linear equations in two variables. The exercise of 3.5 is an important chapter of math of class 10th i solve this question Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:(iv) 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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1. Let x km/h be the speed of car from point A and y km/h be the speed of car from point B.

If the car travels in the same direction,

5x â€“ 5y = 100

x â€“ y = 20 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(i)

If the car travels in the opposite direction,

x + y = 100â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(ii)

Solving equation (i) and (ii), we get

x = 60 km/hâ€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(iii)

Using this in equation (i), we get,

60 â€“ y = 20

y = 40 km/h

Therefore, the speed of car from point A = 60 km/h

Speed of car from point B = 40 km/h.

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