SOLUTION: Stephanie took her kayak to the Kaweah River, which flows downstream at a rate of 2 kilometers per hour. She paddled 15 km upstream, and then paddles downstream to her starting poi
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Question 277019: Stephanie took her kayak to the Kaweah River, which flows downstream at a rate of 2 kilometers per hour. She paddled 15 km upstream, and then paddles downstream to her starting point. If this round-trip took a total of 4 hours, find the speed that Stephanie can paddle in still water.
Found 2 solutions by solver91311, mananth:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
represent the speed in still water. Then let 
represent the elapsed time for the upstream trip. The upstream speed is then 
, the downstream speed is 
, and the downstream time is 
Using the relationship of distance equals rate times time, we can describe the upstream trip:
t)
and the downstream trip is:
(4\ - \t))
Divide both sides of both equations by the rate expression and solve for :
Now we have two expressions equal to , set them equal to each other:
Apply LCD {)
}:
\ -\ 15\left(r\,+\,2\right)}{r^2\,-\,4}\ =\ \frac{15\left(r\,-\,2\right)}{r^2\,-\,4})
\ -\ 15\left(r\,+\,2\right)\ -\ 15\left(r\,-\,2\right)}{r^2\,-\,4}\ =\ 0)
Expand and collect like terms:
Multiply both sides by
Finally, solve the factorable quadratic. Exclude the negative root (she wasn't padding backwards, after all). The positive root is the speed in still water.
John
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Stephanie took her kayak to the Kaweah River, which flows downstream at a rate of 2 kilometers per hour. She paddled 15 km upstream, and then paddles downstream to her starting point. If this round-trip took a total of 4 hours, find the speed that Stephanie can paddle in still water
Let her speed in still water be x
upstream her speed will be x-2 kph
time taken upstream = x/x-2
time taken down stream is x/x+2
15/x-2 +15/x+2= 4 hours
15(x+2)+15(x-2)=4(x+2)(x-2)
15x+30+15x-30=4(x+2)(x-2)
30x=4x^2-16
4x^2-30x-16=0
2x^2-15x-8=0
2x^2-16x+x-8=0
2x(x-8)+1(x-8)=0
(x-8)(2x+1)=0
x=8 rate in still water
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