Question

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

Answer 1

let speed of stream be x km/h
upstream speed of boat (18-x)km/h
downstream speed of boat (18+x)km/h
$\frac{24}{18 - x} = \frac{24}{18 + x} + 1 \\ \frac{24 }{18 - x} = \frac{24 + 18 + x}{18 + x} \\ \frac{42 + x}{18 + x} = \frac{24}{18 - x} \\ (42 + x)(18 - x) = 24(18 + x) \\ 756 - 42x + 18x - {x}^{2} = 432 + 24x \\ 756 - 432 - 24x - {x}^{2} - 24x = 0 \\ 324 - 48x- {x}^{2} = 0 \\ {x}^{2} + 48x - 324 = 0 \\ {x}^{2} + 54x - 6x - 324 = 0 \\ x(x + 54) - 6(x + 54) = 0 \\ (x - 6)(x + 54) = 0 \\ x = 6 \\ x = - 54 \\ discard \: - ve \: value \\ speed \:o f \: stream \: is \: 6kmph$

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 .