Question

A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstrethan to return downstream to the same spot.find the speed of the stram.

Answer 1

Given, speed of the boat in still water = 18 km/hr.

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

Speed of the boat upstream = Speed of boat in still water – Speed of the stream

∴ Speed of the boat upstream = ( 18 – x ) km/hr

Speed of the boat downstream = Speed of boat in still water + Speed of the stream

∴ Speed of the boat downstream = ( 18 + x ) km/hr

Time of upstream journey = Time for downstream journey + 1 hr



⇒ 48x = 324 – x2

⇒ x2 + 48x – 324 = 0



∴ x = 6 (Speed of the stream cannot be negative)

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

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Answer 2

Answer:

Let the speed of stream be x km / hr

For upstream = ( 18 - x ) km / hr

For downstream = ( 18 + x ) km / hr

A.T.Q.

24 / 18 - x - 24 / 18 + x = 1

48 x = 324 - x²

x² + 48 x - 324 = 0

( x + 54 ) ( x - 6 ) = 0

x = - 54 or x = 6

Since speed can't be negative .

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