SOLUTION: Two fishing boats depart a harbor at the same time, one traveling east, the other south. The eastbound boat travels at a speed 7 mi/h faster than the southbound boat. After four ho

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Question 489149: Two fishing boats depart a harbor at the same time, one traveling east, the other south. The eastbound boat travels at a speed 7 mi/h faster than the southbound boat. After four hours the boats are x = 52 mi apart. Find the speed of the southbound boat.
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
4n2+(4(n+7))2=(52)2
4n2+(4n+28)2=2704
4n2+16n2+224n+784=2704
20n2+224n-1920=0
5n2+56n-480=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B56x%2B-480+=+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=%2856%29%5E2-4%2A5%2A-480=12736.

Discriminant d=12736 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-56%2B-sqrt%28+12736+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2856%29%2Bsqrt%28+12736+%29%29%2F2%5C5+=+5.68538878373271
x%5B2%5D+=+%28-%2856%29-sqrt%28+12736+%29%29%2F2%5C5+=+-16.8853887837327

Quadratic expression 5x%5E2%2B56x%2B-480 can be factored:
5x%5E2%2B56x%2B-480+=+5%28x-5.68538878373271%29%2A%28x--16.8853887837327%29
Again, the answer is: 5.68538878373271, -16.8853887837327. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B56%2Ax%2B-480+%29

Throwing out the negative answer, we get the speed of the southbound boat to be 5.68538878373271 mph..