Q30 of 50 Page 1

A motorboat whose speed in still water is 18 km/h, takes 1 hour 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 x km/h.


∴ The speed of the boat upstream = (18 – x) km/h


And the speed of the boat downstream = (18 + x) km/h


We know that time = distance/speed


⇒ Time taken to go upstream hours


Also, time taken to go downstream hours


Given


⇒ 24 (18 + x) – 24 (18 – x) = (18 – x) (18 + x)


⇒ x2 + 48x – 324 = 0


We know that quadratic formula


Using the quadratic formula, we get






= 6 or -54


Since x is the speed of the stream, it cannot be negative.


∴ x = 6 gives the speed of the stream as 6 km/h.


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