Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in same direction, they meet in 8 hours and if they move towards each other they meet in 1 hour 20 minutes. Find the speed of cars.

Let the speed of first car be x km/hr

And the speed of the second car be y km/hr

Given A and B are 80km apart,

a car starts from A and another from B at the same time

Case 1: moving in same direction

The two cars will meet in 8 hours, so

time = 8hrs

Let the two cars meet at point C, so

So, distance travelled by first car = AC

And distance travelled by second car = BC

So, the difference of distance travelled = AC - BC

⇒ AB = 80km is the relative distance

Relative speed will be speed of 1^st car - speed of 2^nd car

⇒ speed = (x - y) km/h

And we know

Distance = speed × time

Substituting the values, we get

80 = (x - y) × 8

⇒ x - y = 10……….(i)

Case 2: moving in opposite direction

The two cars will meet in 1 hour 20 minutes, so

Let the two cars meet at point C, so

So, distance travelled by first car = AC

And distance travelled by second car = BC

So the total distance travelled = AC + BC

⇒ AB = 80km is the relative distance

Relative speed will be speed of 1^st car + speed of 2^nd car

⇒ speed = (x + y) km/h

And we know

Distance = speed × time

Substituting the values, we get

x + y = 60………(ii)

So, the pair of linear equations in two variables are

x + y = 60

x - y = 10

Now we will solve these pair of equations,

Adding the two equations we get

x + y = 60

x - y = 10

2x = 70

⇒ x = 35

Hence the speed of first car is 35 km/hr

Substituting the value of x in first equation, we get

x + y = 60

⇒ 35 + y = 60

⇒ y = 60 - 35

⇒ y = 25

Hence the speed of second car is 25 km/hr.

So, the speed of two cars is 35km/hr and 25km/hr.