# Places A and B ar

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 1st car – the speed of the 2nd 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 1st car + speed of the 2nd 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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