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Question
Distance between two places A and B is 210 km. Two cars start simultaneously from A and B in opposite direction and distance between them after 3 hours is 54 km. If speed of one car is less than that of other by 8 km/hr, find the speed of each.
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Solution
Let the speed of car starts from A be x km/h.
Then, speed of car starts from B = (x + 8) km/h
Given, distance between the cars after 3 h = 54 km
According to the question,
Total distance between A and B – Total distance covered by both cars in 3 h = 54
⇒ 210 – [3x + 3(x + 8)] = 54 ...[∵ Distance = Speed × Time]
⇒ 210 – 3x – 3x – 24 = 54
⇒ – 6x = – 210 + 24 + 54
⇒ – 6x = – 210 + 78
⇒ – 6x = – 132
⇒ x = `- 132 xx ((-1)/6)`
∴ x = 22
Hence, the speed of car starts from A = 22 km/h
And the speed of car starts from B = 22 + 8 = 30 km/h
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