SOLUTION: The current in a stream moves at a speed of 4mi/h. A boat travels 4 miles upstream and 28 km downstream in a total time of 4 hours. What is the speed of the stream?

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Question 442824: The current in a stream moves at a speed of 4mi/h. A boat travels 4 miles upstream and 28 km downstream in a total time of 4 hours. What is the speed of the stream?
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
4/x-4+28/x+4=4
4(x+4)+28(x-4)=4(x2-16)
4x+16+28x-112=4x2-64
0=4x2-32x+32
0=x2-8x+8
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B8+=+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=%28-8%29%5E2-4%2A1%2A8=32.

Discriminant d=32 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+32+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+32+%29%29%2F2%5C1+=+6.82842712474619
x%5B2%5D+=+%28-%28-8%29-sqrt%28+32+%29%29%2F2%5C1+=+1.17157287525381

Quadratic expression 1x%5E2%2B-8x%2B8 can be factored:
1x%5E2%2B-8x%2B8+=+1%28x-6.82842712474619%29%2A%28x-1.17157287525381%29
Again, the answer is: 6.82842712474619, 1.17157287525381. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B8+%29

Throwing out the lower number, we get the speed of the boat in still water to be 6.828 mph..