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On a roadway, points C and D are 90 km away from one another. At the same time, one car begins from C and another from D. They will meet in 9 hours if they travel in the same direction, and in $127$ hours if they travel in the opposite direction. What is the speed of both the cars?

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40 km/h and 30km/h

40 km/h and 50km/h

30 km/h and 30km/h

20 km/h and 40km/h

answer is A.

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Detailed Solution

It is given that two points C and D are 90 km away from one another on a roadway. At the same time, one car begins from C and another from D. They will meet in 9 hours if they travel in the same direction, and in

127

hours if they travel in the opposite direction.
Let’s assume that the speed of the cars starting from C and D be

x

km/h and

y

km/h. According to the question,

9 x − 90 = 9 y ⇒ x − y = 10 (1) and

97 x + 97 y = 90 ⇒ 17 x + 17 y = 10 (2)

Divide equation (1) by 7 and then add with equation (2), we get,

17 x + 17 x = 107 + 10 ⇒ 27 x = 807 ⇒ x = 40

Therefore from equation (1), we have,

x − y = 10 ⇒ 40 − y = 30 ⇒ y = 30

Therefore the speed of the car starting from point C = 40 km/h and the speed of the car starting from point D = 30 km/h.
Hence option (1) is correct.

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