Q26 of 47 Page 1

A motorboat whose speed in still water is 18 km/h takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Let the speed of the stream be y km/h

Upstream = (18 – y) km/h


Downstream = (18 + y) km/h


⸫ Time =


According to question,


⇒


⇒ 24 (18 + y) – 24 (18 – y) = 182 – y2


⇒ 24y + 24y = 324 – y2


⸫ y2 + 48y – 324 = 0


[By splitting the middle term]


⇒ y2 + 54y – 6y – 324 = 0


⇒ y (y + 54) – 6 (y + 54) = 0


⇒ (y + 54) (y – 6) = 0


⇒ y + 54 = 0 or y – 6 = 0


⸫ y = – 54 or y = 6


⸫ The speed of the stream = 6 km/h [⸪ Speed cannot be negative]


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