SOLUTION: I am trying to figure out a word problem (I don't know why but I just can't get how to set up any word problems). Anyway, I need to determine a quadratic equation to solve the pro

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Question 206435: I am trying to figure out a word problem (I don't know why but I just can't get how to set up any word problems). Anyway, I need to determine a quadratic equation to solve the problem and then solve the problem. My word problem is as follows:
A river has a current of 5mph. It takes Al half an hour longer to paddle upstreat 1.2 miles than to paddly downstram the same distance. What is Al's rate is still water?
In attempt to set up the problem I am doing the following:
P = Paddle
(p+5)(p-5)
The trip upstream takes 1/2 hour longer
(1.5)/(p-5) + (1.5)/(p+5) = 0
Am I on the right track? Any suggestions on how to set up word problems - I have such difficulty no matter what the problem is.
Thanks - Lori

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A river has a current of 5mph.
It takes Al half an hour longer to paddle upstream 1.2 miles than to paddle
downstream the same distance.
What is Al's rate is still water?
:
Your initial format made sense, however, after that you lost me, my take on this:
:
Let p = speed in still water
;
down time + half hour = up time
+ .5 =
multiply eq by (p+5)(p-5), resulting in:
:
1.2(p-5) + .5(p-5)(p+5) = 1.2(p+5)
:
1.2p - 6 + .5(p^2 - 25) = 1.2p + 6
:
1.2p - 6 + .5p^2 - 12.5 = 1.2p + 6
Arrange as a quadratic equation on the left
.5p^2 + 1.2p - 1.2p - 6 - 6 - 12.5 = 0
:
.5p^2 - 24.5 = 0
Multiply by 2 to get a rid of the fraction
p^2 - 49 = 0
The difference of squares
p = -7
p = +7, the solution we want
:
7 mph in still water
:
:
Is this true, find the times
1.2/(7+5) = .1 hrs
1.2/(7-5) = .6 hrs
-------------------
a difference of .5 hrs