Answer :

Let the speed of the 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 the same direction

The two cars will meet in 8 hours, so

time = 8hrs

Let the two cars meet at point C, so

So, distance traveled by the first car = AC

And distance traveled by the second car = BC

So, the difference in distance traveled = AC – BC

⇒ AB = 80km is the relative distance

Relative speed will be the speed of the 1^{st} car – the speed of the 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 the opposite direction

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

Let the two cars meet at point C, so

So, distance traveled by the first car = AC

And distance traveled by the second car = BC

So the total distance traveled = AC + BC

⇒ AB = 80km is the relative distance

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

⇒ speed = (x + y) km/h

And we know

Distance = speed × time

Substituting the values, we get

⇒ 20 × 3 = (x+y)

⇒ 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 = 35

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

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

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