Question

Points A and B on a national highway are at a distance of 120 km from each other. One car starts from A and another from B at the same time. The car which starts from A moves with a constant speed along the direction AB and the second moves with a constant speed in the same direction from B. The first car overtakes the second car in 4 hours.however, if the second car moves from B towards A then the two meet each other after hours 2 hours. Find the speed of the car which starts from A.​

Answer 1

Answer:

45 km/hr

Step-by-step explanation:

Given  

Points A and B on a national highway are at a distance of 120 km from each other. One car starts from A and another from B at the same time. The car  which starts from A moves with a constant speed along the direction AB and the second moves with a constant speed in the same direction from B. The first car overtakes the second car in 4 hours.however, if the second car moves from B towards A then the two meet each other after hours 2 hours. Find the speed of the car which starts from A.​

ANSWER

Let the speed of the car starting from point A be x and speed of the car starting from point B be y km/hr and distance AB = 120 km

If both cars move in same direction AB, first car overtakes second car in 4 hrs. So distance covered by first car in 4 hrs is 120 km more to the distance covered by second car. Distance = speed x time.

So 4 x = 4 y + 120

      4 x – 4 y = 120

        x – y = 30----------(1)

So if they move towards each other, they meet in 2 hrs.

So distance covered by first and second car in 2 hrs is 120 km

 2 x + 2 y = 120

   x + y = 60------------(2)

Solving equations 1 and 2 we get

 2 x = 90

  x = 90/2

 x = 45

x – y = 30

45 – y = 30

 45 – 30 = y

  y = 15

So the speed of the car which starts from A is 45 km/hr