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Solution


Q.

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

Ans.

(6)

Let the speed of the stream be x km/h.

Therefore, the speed of the boat upstream = (18 – x) km/h and the speed of the boat downstream = (18 + x) km/h.

The time taken to go upstream = distance/speed = 2418+x

Similarly, the time taken to go downstream = 2418-x

According to the question, 2418-x-2418+x=1

⇒24(18+x)-24(18-x)=(18-x)(18+x)⇒x2+48x-324=0⇒x=6 or -54

Since x is the speed of the stream, it cannot be negative. So, we ignore the root x = – 54. Therefore, x = 6 gives the speed of the stream as 6 km/h.