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

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) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=12736 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5.68538878373271, -16.8853887837327. Here's your graph:

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