SOLUTION: the speed of the boat in still water is 11km/hr.it can go 12km upstream and return downstream to the original point in 2hrs 45min. find the speed of the stream.

Question 620028: the speed of the boat in still water is 11km/hr.it can go 12km upstream and return downstream to the original point in 2hrs 45min. find the speed of the stream.
Found 2 solutions by lwsshak3, josmiceli:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
the speed of the boat in still water is 11km/hr.it can go 12km upstream and return downstream to the original point in 2hrs 45min. find the speed of the stream.
**
let x=speed of stream
11+x=speed of boat downstream
11-x=speed of boat upstream
2 hr and 45 min=2.75 hr
Travel time=distance/speed
**
12/(11+x)+12/(11-x)=2.75
LCD:(11+x)(11-x)
12(11-x)+12(11+x)=2.75(11+x)(11-x)=2.75(121-x^2)=332.75-2.75x^2
132-12x+132+12x=332.75-2.75x^2
264=332.75-2.75x^2
2.75x^2=332.75-264=68.75
x^2=68.75/2.75=25
x=5
speed of stream= 5 km/hr
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
For now,
Let = the speed of the boat in still water
Let = the speed of the stream
= the speed of the boat going downstream
= the speed of the boat going upstream
Let = time for the boat to travel upstream
= time to travel downstream ( is 2 hrs 45 min )
------------------------
Going upstream:
(1)
Going downstream:
(2)
-----------------------
It is given that
(1)
(1)
and
(2)
(2)
(2)
(2)
From (1),
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
The speed of the stream is 5 km/hr
check:
(1)
(1)
(1)
(1) hrs
and
(2)
(2)
(2)
(2)
(2)
OK
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