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)   (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 (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=6920 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 45.7966343430854, 4.20336565691458. Here's your graph:

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