Question

swati can row her boat at a speed of 5km /h in still water . if it takes her 1hour more to row the boat 5.25km upstream then to returnes downstream .find the speed of the stream

Answer 1

Let the speed of stream be "x" km/h
Now speed down stream = 5 + x km/h
And speed up stream = 5 - x km/h  ( as speed of boat > speed of stream )
Now as time = distance / speed
By substituting we get, :-

5.25/5+x - 5.25/5-x = 1
By solving the equation , we get  

4x^2 + 42x - 100 = 0
By solving this by +50x and - 8x
we get ,

(2x-4)(2x + 25) = 0
Hence x = -25/2 or 2
As speed cant be in negative
Speed of stream = 2 km/ hr

HOPE IT HELPS YOU.
ALL THE BEST.

Answer 2

Let the speed of the stream be x.

the Speed of the boat upstream = (5 - x) km/hr.

the Speed of the boat downstream = (5 + x)km/hr.

Given that It takes 1 hour more to row the boat 5.25km upstream than to return downstream.

5.25/(5 - x) = 5.25/(5 + x) + 1

525/(5 - x) = 525/(5 + x) + 100

525(5 + x) = 525(5 - x) + 100(5 + x)(5 - x)

525x + 2625 = 2625 - 525x + 100(25 - x^2)

525x + 2625 = 2625 - 525x + 2500 - 100x^2

100x^2 + 1050x - 2500 = 0

50(2x^2 + 21x - 50) = 0

2x^2 + 21x - 50

2x^2 - 4x + 25x - 50

2x(x - 2) + 25(x - 2) = 0

(x - 2) = 0 (or) 2x + 25 = 0

x = 2 (or) x = -25/2.


Therefore the speed of the stream = 2km/hr.

Hope this helps!