Question

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

Answer 1

Answer:

Time = Distance/speed

Given, motorboat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km upstream that to return downstream to the same spot.

Let the speed of stream be ‘a’ km/hr.

Relative speed of boat going upstream = 18 – a km/hr

Relative speed of boat going downstream = 18 + a km/hr

⇒ 24(18 + a – 18 + a) = -a2 + 324

⇒ a2 + 48a – 324 = 0

⇒ a2 + 54a - 6a – 324 = 0

⇒ a(a + 54) – 6(a + 54) = 0

⇒ (a – 6)(a + 54) = 0

⇒ a = 6 km/hr

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 .