SOLUTION: during the first part of a trip a canoeist travels 68 miles at a certain speed. The canoeist travels 3 miles on the second part of the trip at a speed of 5 mph slower the total ti

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Question 478422: during the first part of a trip a canoeist travels 68 miles at a certain speed. The canoeist travels 3 miles on the second part of the trip at a speed of 5 mph slower the total time for the trip is 3 hours 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!
68/(p+5)+3/p=3
68p+3(p+5)=3p(p+5)
68p+3p+15=3p2+15p
3p2-56p+15=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-56x%2B15+=+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=%28-56%29%5E2-4%2A3%2A15=2956.

Discriminant d=2956 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--56%2B-sqrt%28+2956+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-56%29%2Bsqrt%28+2956+%29%29%2F2%5C3+=+18.3948514793788
x%5B2%5D+=+%28-%28-56%29-sqrt%28+2956+%29%29%2F2%5C3+=+0.271815187287875

Quadratic expression 3x%5E2%2B-56x%2B15 can be factored:
3x%5E2%2B-56x%2B15+=+3%28x-18.3948514793788%29%2A%28x-0.271815187287875%29
Again, the answer is: 18.3948514793788, 0.271815187287875. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-56%2Ax%2B15+%29

p=18.3948514793788 or 0.27181518728787
Throwing out the smaller answer, we get the speed of the boat on the second part of the trip to be 18.3948514793788 mph. On the first part it was 23.3948514793788 mph..