Places A and B are apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in and if they move in opposite directions, they meet in . Find the speeds of the cars.

Let the speed of the car leaving A to be ‘x’ km/h and the speed of the car leaving B to be ‘y’ km/h.

Total distance=80 km

Also 1 hour 20 mins= 4/3 hour

When an automobile goes in the same direction as a specified condition,

Distance travelled by y= 8y km

Distance travelled by x= 8x= 80+8y

Now, Equation formed is 8x=80+8y

 8x-8y=80

 x-y=10 —-(1)

Similarly, For opposite direction,

Distance travelled by x= (4/3)x

Distance travelled by y= (4/3) y

Also total distance covered= 4/3 x+4/3y

80= 4x+4y/3

240= 4x+4y

60=x+y —-(2)

Solving Equation (1) and (2)

60=x+y —-(2)

x-y=10 —-(1)

 x= 10+y —-(3)

Substituting the value of (3) in (2) we get,

60= 10+y+y

 60-10=2y

 50=2y

 25=y

Also we know that, x=10+y=> x= 10+25=> x=35

Thus, Speed of car starting from A is 35km/h

Speed of car starting from B is 25km/h