Question

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

Answer 1

Let , speed of Stream is x km/h.

Than,

→ upstream Speed = (18 - x) km/h.

→ Downstream speed = (18 + x) km/h.

So,

→ Upstream Time - Downstream Time = 1 Hour ,

Putting values we get :-

→ 24/(18-x) - 24/(18+x) = 1

→ (18+x - 18 + x) /(324 - x²) = 1/24

→ 2x * 24 = 324 - x²

→ x² + 48x - 324 = 0

→ x² + 54x - 6x - 324 = 0

→ x(x+54) - 6(x+54) = 0

→ (x+54)(x - 6) = 0

Putting Both Equal to zero now, we get,

→ x = (-54) & 6 .

Since, Speed cant be in Negative.

Hence, We can conclude That, Speed of Stream is 6km/h.

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 .