4. 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 1st car and 2nd car be u km/h and v km/h.
Respective speed of both cars while they are travelling in same direction = (u - v) km/h
Respective speed of both cars while they are travelling in opposite directions i.e., travelling towards each other = (u + v) km/h
According to the question,
5(u - v) = 100
⇒ u - v = 20 ... (i)
1(u + v) = 100 ... (ii)
Adding both the equations, we get
2u = 120
u = 60 km/h ... (iii)
Putting this value in equation (ii), we obtain
v = 40 km/h
Hence, speed of one car = 60 km/h and speed of other car = 40 km/h
