Question

a motor boat whose speed is 18 km/h in still water takes 1h more to go 24 km upstream than ro returm downstream to the same spot. find the speed of stream.

Answer 1

Let the speed of stream be x km/hr.
Now the speed of boat and stream (For Upstream) = (18 - x)km/hr
Now the speed of boat and stream (For Downstream) = (18 + x)km/hr
Time = Distance/Speed

Time Upstream = 24/18-x  ----------- T₁
Time Downstream = 24/18+x  ------- T₂

ACCORDING TO THE QUESTION,

Time = 1hr

T₁ = T₂ + 1hr

T₁ - T₂ = 1hr

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

24(18+x) - 24(18-x) / (18-x)(18+x) = 1
432 + 24x - 432 + 24x = 18² - x²      [(a+b)(a-b) = (a²-b²)]
x² + 48x - 324 = 0
x² - 6x + 54x - 324 = 0
x(x-6) + 54(x-6) = 0
(x-6) (x+54) = 0
x - 6 = 0  or  x + 54 = 0

x = 6  or  x = -54

But speed cannot be NEGATIVE,
Hence Speed of the stream is 6km/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 .