Question

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

Answer 1

Hey

Here is your answer,

Lets take speed of the stream to be 'x' km/hr. 

So, net upstream speed=(18-x)km/hr
And net downstream speed=(18+x)km/hr
Distance = 24km. 
So, time taken to go upstream 24km = 24/(18-x)
And time taken to go downstream 24km= 24/(18+x)

Given : 24/(18-x)=1+24/(18+x)

So, 24/(18-x)=(18+x+24)/(18+x)

= 24(18+x)=(42+x)(18-x)
= 432+24x=756-24x-x^2
= x^2 +48x-324=0

Solving the quadratic, you will get x to be 6 or -54, but speed cant be
negative,

So the stream's speed is 6km/hr.

Hope it helps you!

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 .