point a and b are 70km a part on a highway.a car starts from a and another car stars from b simultaneously if they travel in the same direction they meet in 7 hours,but if they travel towords each other they meet in one hour.find the speed of the two cars.
Answers
ANSWER:
Given:
- Distance between A and B = 70km
- 2 cars are on point A and B.
- Time taken to meet when they move in same direction = 7hrs
- Time taken to meet when they move towards each other = 1hr
To Find:
- Speed of both cars.
Solution:
Let the speed of car 1 be x km/hr and speed of car 2 be y km/hr.
We are given that,
⇒ Time taken to meet when they move in same direction = 7hrs
And,
⇒ Time taken to meet when they move towards each other = 1hr
Now, in first case, time taken is more than the second case.
This means, the net speed in first case is less than the net speed in second case.
⇒ Net speed in 1st case = (x - y) km/hr
⇒ Net speed in 2nd case = (x + y) km/hr
We know that,
⇒ Speed = Distance/Time.
Here distance is 70km and time is 7hr and 1 hr in cases 1 and 2 respectively.
Case 1:
⇒ Speed = Distance/Time.
⇒ x - y = 70/7
⇒ x - y = 10 ------(1)
Case 2:
⇒ Speed = Distance/Time.
⇒ x + y = 70/1
⇒ x + y = 70 ------(2)
Adding (1) and (2),
⇒ x - y + x + y = 10 + 70
⇒ 2x = 80
⇒ x = 40
Substituting value if x in (2),
⇒ x + y = 70
⇒ 40 + y = 70
⇒ y = 70 - 40
⇒ y = 30
Hence, speed of Car 1 and Car 2 is 40km/hr and 30km/hr respectively.