Places A and B are 20 km apart on the highway. A car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in one hour. If they travelled towards each other, they meet in 12 minutes. What are the speeds (in km/h) of two cars?

Options
a) 52, 48
b) 55, 45
c) 60, 40
d) 51, 49

Solution

As per question
Distance = 20 km
Time = 1 hour
Relative speed in car (i) = 20/1 = 20 km/h
S₁ – S₂ = 20 _____(1)
Relative speed in car (ii) = 20/12/60 = = 100 km
S₁ + S₂ = 100 _____(2)

Equation (2) – (1)
(S₁ + S₂) – (S₁ – S₂) = 100 – 20
S₁ + S₂ – S₁ + S₂ = 80
2 S₂ = 80
S₂ = 40
From equation to
S₁ + S₂ = 100
S₁ + 40 = 100
S₁ = 100 – 40
S₁ = 60

Answer: c) 60, 40