Car 'A' is at point 'P' while car 'B' is at point 'Q'. Both the cars started travelling towards each other at the same time such that they met each other after 8 hours. However, if both car start at the same time but travel in the same direction, then they will meet after 40 hours. If the speed of the slower car is 60 km/h, then which of the following statement(s) is/are true?

I. Distance between point 'P' and 'Q' is 1500 km.

II. While travelling in opposite directions, the faster car covers 720 km by the time they meet.

III. The faster car is twice as fast as the slower car.

Solution

Let the distance between points 'P' and 'Q' be 'd' km. Let the speed of faster car and slower car be 'x' km/h and 'y' km/h, respectively. ATQ; {d/(x + y) } = 8 ........ (I) {d/(x - y) } = 40 ...... (II) So, 40 X (x - y) = 8 X (x + y) Or, 40x - 40y = 8x + 8y Or, 32x = 48y So, (x/y) = (3/2) So, speed of faster car = 60 X (3/2) = 90 km/h So, 'd' = (90 + 60) X 8 = 1200 For 'I': Distance between 'P' and 'Q' = 1200 km So, 'I' is false. For 'II': Distance covered by faster car when travelling in opposite directions = 1200 X (3/5) = 720 km So, 'II' is true. For 'III': Speed of faster car = 90 km/h And, speed of the slower car = 60 km/h Speed of faster car = 1.5 x speed of slower car So, 'III' is false.