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 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.