Question

a motorboat whose speed is 18 km per hour is still in water takes 1 hour more to go 24 km upstream than to return downstream to the same spot .find the the speed of the stream

Answer 1

Given, speed of the boat in still water = 18 km/hr.

Let the speed of the stream be x km/hr.

Speed of the boat upstream = Speed of boat in still water – Speed of the stream

∴ Speed of the boat upstream = ( 18 – x ) km/hr

Speed of the boat downstream = Speed of boat in still water + Speed of the stream

∴ Speed of the boat downstream = ( 18 + x ) km/hr

Time of upstream journey = Time for downstream journey + 1 hr

*The image will be the answer in this part..

⇒ 48x = 324 – x2 

⇒ x2 + 48x – 324 = 0

=>x²+54x-6x-324=0

=>x(x+54)-6(x+54)=0

=>(x-6)(x+54)=0

=>Either, || Or,
x=6, x=-54(The negative value is ignored)

∴ x = 6  (Speed of the stream cannot be negative)

Thus, the speed of stream is 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 .