SOLUTION: Please help me solve this: During the first part of a trip, a canoeist travels 36 miles at a certain speed. The canoeist travels 8 miles on the second part of the trip at a speed

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Question 502927: Please help me solve this: During the first part of a trip, a canoeist travels 36 miles at a certain speed. The canoeist travels 8 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hours. What was the speed on each part of the trip?
I have tried example problems that are similar but I seem to not understand this process. Thanks in advance for helping.
Answer by jrb1965(16) About Me  (Show Source):
You can put this solution on YOUR website!
Distance = Rate * Time
Let S1 be the speed on part 1, and S2 be the speed on part 2
Given S2 = S1 - 5
Given T1 + T2 = 5, so T2 = 5 - T1
36 = S1 * T1, so T1 = 36/S1
8 = S2 * T2
Substituting the first 3 equations in the form of S1 into the 4th equation
8 = (S1 - 5) * (5 - (36/S1)) = 5S1 - 36 - 25 + (180/S1)
Multiply all terms by S1 to get the quadratic equation
5S1%5E2 - 69S1 + 180 = 0
Use the quadratic formula S1+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a = 5, b = -69, c = 180
so S1 = 10.3 MPH (if you use the other solution, S2 would be negative)
S2 = 5.3 MPH
T1 = 3.5 Hours
T2 = 1.5 Hours