Points A and B are 90 km apart from each other on a highway. Car X starts from point A and another car Y starts from point B at the same time. If they travel in the same direction they meet in 9 hours and if they travel in opposite directions they meet in 97 hours. What is the speed of car X?
The correct option is
Let X and Y be two cars starting from points A and B respectively. Let the speed of car X be x km/hr and that of car Y be y km/hr.
Case I: When the two cars move in the same direction:
Suppose two cars meet at point Q.
Distance travelled by car X = AQ
Distance travelled by car Y = BQ
∴ Distance travelled by car X in 9 hours = 9x km ⇒ AQ = 9x
Distance travelled by car Y in 9 hours = 9y km ⇒ BQ = 9y
Clearly, AQ - BQ = AB [∵ AB = 90 km]
⇒ 9x - 9y = 90 ⇒ x - y = 10 . . . . (1)
Case II: When two cars move in opposite direction:
Suppose two cars meet at point P.
Distance travelled by car X = AP.
Distance travelled by car Y = BP.
In this case, two cars meet in 97 hours.
Distance travelled by car X in 97hours=97x km ⇒ AP=97x
Distance travelled by car Y in 97hours=97y km ⇒ BP=97y
Clearly, AP + BP = AB
⇒ x + y = 70 . . . . (2)
Adding equations (1) and (2),
x - y = 10 ....(1)
x + y = 70 .....(2)
⇒ 2x = 80
⇒ x = 40
Substitute x = 40 in eq. (1)
40 - y = 10
y = 40 - 10 = 30
∴ x = 40 and y = 30
Hence, speed of car starting from point A is 40 km/hr.