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

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 figureÂ AC â€“ BC = 160

â‡’ x Ã— 8 â€“ y Ã— 8 = 160

â‡’ x â€“ y = 20

Case-2: When they travel in opposite direction

From the figureÂ AC + BC = 160

â‡’ x Ã— 2 + y Ã— 2 = 160

â‡’ x + y = 80

Adding (i) and (ii), we getÂ 2x = 100Â â‡’ x = 50 km/h

Putting x = 50 in (ii), we have

50 + y = 80

â‡’ y = 80 â€“ 50 = 30 km/h

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