Q4. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :
(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Let the speed of the first car is x and the speed of the second car is y.
Let's solve this problem by using relative motion concept,
the relative speed when they are going in the same direction= x - y
the relative speed when they are going in the opposite direction= x + y
The given relative distance between them = 100 km.
Now, As we know,
Relative distance = Relative speed * time .
So, According to the question,
Now Adding (1) and (2) we get
putting this in (1)
Hence the speeds of the cars are 40 km/hour and 60 km/hour.