A steamer goes downstream from one port to another in 2 hours. It covers the same distance upstream in 3 hours. If the speed of stream is 4 km/h, the distance between the two ports is
Solution
Correct Answer: Option D
Let the distance from one port to another is = d
Let speed of boat is = x
Given, time in downstream = 2 hr
∵ Time = distance/(Speed in downstream)
Speed of motorboat in downstream = speed of boat + speed of stream
∴ speed of motorboat in downstream = x + 4
∴ 2 = d/(x + 4)
⇒ d = 2x + 8
Given, time in upstream = 3 hr
∵ Time = distance/(speed in upstream)
Speed of motorboat in upstream = speed of boat – speed of stream
∴ speed of motorboat in upstream = x – 4
∴3 = d/(x - 4)
⇒ d = 3x – 12
Distance will be equal so
⇒ 2x + 8 = 3x – 12
⇒ x = 20
∵ Distance = speed × time
⇒ d = (20 – 4) × 3
⇒ d = 48 km
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