Q. 244.0( 15 Votes )
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 direction, they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.
Let the speed of the 1st car at point A and 2nd car at point B travelling in positive x - axis direction be x and y respectively.
Case 1: Same Direction
Distance Travelled by 1st and 2nd Car in 8 hours are 8x and 8y respectively.
Both the cars will meet outside of the points A and B which are 160 km apart. So, the 1st car will travel 160 km more distance from 2nd car meeting each other in 8 hours.
∴ 8x - 8y = 160
⇒ x - y = 20.....(1)
Case 2: Opposite Direction
Distance Travelled by 1st and 2nd Car in 2 hours are 2x and 2y respectively.
Both the cars will meet in between the points A and B which are 160 km apart. So, the sum of distance travelled by 1st car and distance travelled by 2nd car meeting each other in 2 hours is equal to 160 km.
∴ 2x + 2y = 160
⇒ x + y = 80.....(2)
Adding equations (1) and (2), we get -
2x = 100
∴ x = 50
substitute the value of x in equation (2), we get -
y = 30
Thus, the speed of 1st car = 50 km/h
and, the speed of 2nd car = 30 km/h
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