Question

a motar boat whose speed is 18km/hr in still water takes 1hr more to go 24/km upstream than to return downstraem to the same spot. find the speed of the stream

Answer 1

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Answer 2

Let the speed of the stream be x km/hr

Speed of the boat in still water = 18 km/hr

Speed of the boat in upstream = (18 - x) km/hr

Speed of the boat in downstram = (18 + x) km/hr

Distance between the places is 24 km.

Time to travel in upstream = d / (18 - x) hr

Time to travel in downstream = d / (18 + x) hr

Difference between timings = 1 hr
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According to ques,

[24 / (18 - x)] - [24 / (18 + x)] = 1

⇒ 24 [1 / (18 - x)] - [1 / (18 + x)] = 1

⇒ [1 / (18 - x)] - [1 / (18 + x)] = 1/24

⇒ (18 + x - 18 + x) / (324 - x²) = 1/24

⇒ (2x) / (324 - x²) = 1/24

⇒ 324 - x² = 48x

⇒ x² - 48x + 324 = 0

⇒ (x + 54)(x - 6) = 0

x = - 54 or 6

Speed of the stream can not be negative.

Therefore, speed of the stream is 6 km/hr.

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