Places A and B are 45 km apart from each other. A car starts from place A and another car starts from place B at the same time. If they move in the same direction, they meet in 4 and a half hour and if they move towards each other, they meet in 27 minutes. What is the speed (in km/h) of the car which moves faster?
55
Given:
Distance between the places A & B is 45km.
Moving in the same direction, they take 4.5 i.e. 9/2 hours to meet.
Moving in the opposite direction, they take 27 mins i.e., 27/60 hours to meet.
Concept used:
Distance = Time × Speed
The relative speed of two objects in the same direction is the difference of their speed.
The relative speed of two objects in the opposite direction is the sum of their speed.
Calculation:
Let the speed of the faster & slower car be S a & S b respectively.
Relative speed of the cars when going in the same direction = (S a - S b)
Relative speed of the cars when going in the opposite direction = (S a + S b )
According to the question,
45/ (S a - S b ) = 4.5
⇒ 45/ (S a - S b ) = 9/2
⇒ (S a - S b ) = 10 ....(1)
45/(S a + S b ) = 27/60
⇒ 45/ (S a + S b ) = 9/20
⇒ (S a + S b ) = 100 ....(2)
(1) ÷ (2),
S a = 55
∴ T he speed (in km/h) of the car which moves faster is 55kmph.
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