SOLUTION: During the first part of a trip a canoeist travels 60 miles at a certain speed. The canoeist travels 9 miles on the second part of the trip at a speed of 5mph slower. The total tim

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Question 442398: During the first part of a trip a canoeist travels 60 miles at a certain speed. The canoeist travels 9 miles on the second part of the trip at a speed of 5mph slower. The total time for the trip is 4hrs. 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!
60/x+9/x-5=4
60x-300+9x=4x2-20x
0=4x2-89x+300
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-89x%2B300+=+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=%28-89%29%5E2-4%2A4%2A300=3121.

Discriminant d=3121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--89%2B-sqrt%28+3121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-89%29%2Bsqrt%28+3121+%29%29%2F2%5C4+=+18.1082388617317
x%5B2%5D+=+%28-%28-89%29-sqrt%28+3121+%29%29%2F2%5C4+=+4.14176113826829

Quadratic expression 4x%5E2%2B-89x%2B300 can be factored:
4x%5E2%2B-89x%2B300+=+4%28x-18.1082388617317%29%2A%28x-4.14176113826829%29
Again, the answer is: 18.1082388617317, 4.14176113826829. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-89%2Ax%2B300+%29

Throwing out the 4.1 answer, we get the speed of the canoe to be 18.108 going and 13.108 on the second part of the trip.