Question

Two places A and B are 120 km apart from each other on a highway. A car start from A and another from B at the same time. If they move in same direction, they meet in 6 hours and if they move in opposite directions they meet in 1 hour and 12 minutes. Find the speeds of the car.

Answer 1

Case 1: Both cars move in same direction
Both cars meet in 6 hours
Distance covered by car A in 6 hours = 6x km
Distance covered by car B in 6 hours = 6y km.

For A to meet B in 6 hours, A has to travel a distance of 120 km + 6y km.
$\therefore$ 6x = 120 + 6y
$\therefore$ 6(x-y)=120
$\therefore$ x-y=120 -------------(1)

Case 2: Both cars move in opposite directions
Both cars meet in the $12mins\to 1\frac{1}{5}=\frac{6}{5}hours$.
Distance covered by car A in $\frac{6}{5}hours=\frac{6}{5}$ x. km.
Distance covered by can B is in $\frac{6}{5}hours=\frac{6}{5}ykm$.



$\frac{6}{5}x+\frac{6}{5}y=120$
$\therefore$ x+y = 100 --------(2)
Eqn (1) + eqn (2)
$x-\text{/}yx+\text{/}y=20+100$
$2x=120$
x= 60 km/hr.
$x-y=20\Rightarrow$ $y=x-20=60-20$
$\therefore y=40km/hr$.