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Answer 1

Let velocity of A be v₁ and of B be v₂.

Case - 1 :

relative velocity = v₁ - v₂

(v₁ - v₂) * 5 hrs = 100 km

v₁ - v₂ = 20km/h

Case 2 :

relative velocity = v₁ + v₂

(v₁ + v₂) * 1 hr = 100 km

v₁ + v₂ = 100km/h

Solving both equations,

v₁ = 60km/h

v₂ = 40km/h

Answer 2

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Solution: Let us assume that the speed of car A is x and that of car B is y.

First condition: When both the cars are going in the same direction, their relative speed is; x – y

Hence,

100=(x-y)5

Or, 5x-5y=100

Or, x-y=20

Second condition: When the cars are moving towards each other, their relative speed is; x + y

Hence;

100=x+y

Or, x+y=100

Adding the two equations, we get;

x–y+x+y=20+100

Or, 2x=120

Or, x=60

Substituting the value of x in first equation, we get;

x–y=20

Or, 60–y=20

Or, y=60–20=40

Hence, speed of car A = 60 km/h and speed of car B = 40 km/h

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