Question

Place A and B are 160 km apart on a highway.One car starts from A and another from B at the same time.If they travel in the same direction,they meet in 8 hours.But,If they travel towards each other,they meet in 2 hours.Find the speed of each car.

Answer 1

Sol:
Let the speeds of the cars be x km/hr and y km/hr

Case 1:
When the cars are going in the same direction
Relative speed $=x-y$
Distance = 160 km
Time $=\frac{160}{(x-y)}=8$ hrs
$x-y=\frac{160}{8}=20$
$x–y=20$------------- (1)

Case 2:
When the cars are going in the opposite direction
Relative speed $=x+y$
Time $=\frac{160}{(x+y)}=2$ hrs
$x+y=80$ ------------- (2)

Solving the equations (1) and (2),
x = 50
y = 30
Hence the speeds of the cars are 50 km/hr and 30 km/hr.