SOLUTION: Nancy traveled 6 miles upstream to do some fly fishing. It took her 20 minutes longer to get there than to return. If the current in the river is 2 miles per hour, then how fast wi

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Question 433314: Nancy traveled 6 miles upstream to do some fly fishing. It took her 20 minutes longer to get there than to return. If the current in the river is 2 miles per hour, then how fast will her boat go in still water.
Found 2 solutions by stanbon, jorel1380:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Nancy traveled 6 miles upstream to do some fly fishing. It took her 20 minutes longer to get there than to return. If the current in the river is 2 miles per hour, then how fast will her boat go in still water.
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Upstream DATA:
distance = 6 miles ; rate = b-2 mph; time = 6/(b-2) hrs
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Downstream DATA:
distance = 6 miles; rate = b+2 mph; time = 6/(b+2) mph
-----------------------
Equation:
time up - time down = 1/3 hr
----
6/(b-2) - 6/(b+2) = 1/3
----
Multiply thru by 3(b^2-9) to get:
---
18(b+2)-18(b-2) = b^2-9
----
72 = b^2-9
------
b^2= 81
b = 9 mph (speed of the boat in still water)
=============
Cheers,
Stan H.

Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
To find Nancy's rate of travel, we have to solve for:
6/x-2=6/(x+2)+1/3hr.
Multiply both sides by 3(x-2)(x+2), we get:
18(x+2)=18(x-2)+x2-4
18x+36=18x-36+x2-4
0=x2-76
76=x2
√76=x
√4√19=x
2√19=x
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Nancy's boat goes about 8.72 mph in still water.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-76+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A1%2A-76=304.

Discriminant d=304 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+304+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+304+%29%29%2F2%5C1+=+8.71779788708135
x%5B2%5D+=+%28-%280%29-sqrt%28+304+%29%29%2F2%5C1+=+-8.71779788708135

Quadratic expression 1x%5E2%2B0x%2B-76 can be factored:
1x%5E2%2B0x%2B-76+=+1%28x-8.71779788708135%29%2A%28x--8.71779788708135%29
Again, the answer is: 8.71779788708135, -8.71779788708135. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-76+%29