Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours. But, if they travel towards each other, they meet in 1 hour. 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 7 hours are 7x and 7y respectively.
Both the cars will meet outside of the points A and B which are 70 km apart. So, the 1st car will travel 70 km more distance from 2nd car meeting each other in 7 hours.
∴ 7x - 7y = 70
⇒ x - y = 10.....(1)
Case 2: Opposite Direction
Distance Travelled by 1st and 2nd Car in 1 hours are x and y respectively.
Both the cars will meet in between the points A and B which are 70 km apart. So, the sum of distance travelled by 1st car and distance travelled by 2nd car meeting each other in 1 hours is equal to 70 km.
∴ x + y = 70 .....(2)
Adding equations (1) and (2), we get -
2x = 80
∴ x = 40
substitute the value of x in equation (2), we get -
y = 30
Thus, the speed of 1st car = 40 km/h
and, the speed of 2nd car = 30 km/h