Question 206435
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
{{{1.2/((p+5))}}} + .5 = {{{1.2/((p-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
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a difference of .5 hrs