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# Places A and B are 160 km apart on a highway. one car starts from A and another from B at the same time. If they travel in the same directiin, they meet in 8hrs. But, if they travel towqrds earch other, they meet in 2 hers. Find the speed of each car.

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This is the basic and conceptual question from linear equations in two variables in which we have to find the speed of each car if they travel in the same direction they meet after 8 hrs but if they travel in opposite directions they meet after 2 hrs and the distance between them is 160 km.

Kindly give me a detailed solution of this question

RS Aggarwal, Class 10, chapter 3E, question no 34

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1. Let the speed of the car A and B be x km/h and y km/h respectively.

Let x > y.

Case-1: When they travel in the same direction

From the figure  AC – BC = 160

⇒ x × 8 – y × 8 = 160

⇒ x – y = 20

Case-2: When they travel in opposite direction

From the figure  AC + BC = 160

⇒ x × 2 + y × 2 = 160

⇒ x + y = 80

Adding (i) and (ii), we get  2x = 100  ⇒ x = 50 km/h

Putting x = 50 in (ii), we have

50 + y = 80

⇒ y = 80 – 50 = 30 km/h

Hence, the speeds of the cars are 50 km/h and 30 km/h.

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