SOLUTION: During the first part of a trip, a canoeist travels 77 miles at a certain speed. the canoeist travels 13 miles on teh second part of the trip at a speed 5 mph slower. the total t

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Question 440201: During the first part of a trip, a canoeist travels 77 miles at a certain speed. the canoeist travels 13 miles on teh second part of the trip at a speed 5 mph slower. the total time for the trip is 2 hrs. what was the speed on each part of the trip?
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
77/x+13/x-5=2
77(x-5)+13x=2(x)(x-5)
77x-385+13x=2x2-10x
0=2x2-100x+385
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-100x%2B385+=+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=%28-100%29%5E2-4%2A2%2A385=6920.

Discriminant d=6920 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--100%2B-sqrt%28+6920+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-100%29%2Bsqrt%28+6920+%29%29%2F2%5C2+=+45.7966343430854
x%5B2%5D+=+%28-%28-100%29-sqrt%28+6920+%29%29%2F2%5C2+=+4.20336565691458

Quadratic expression 2x%5E2%2B-100x%2B385 can be factored:
2x%5E2%2B-100x%2B385+=+2%28x-45.7966343430854%29%2A%28x-4.20336565691458%29
Again, the answer is: 45.7966343430854, 4.20336565691458. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-100%2Ax%2B385+%29

Checking for time, we find that x=45.80 is our speed.