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

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) (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
5 - 69 + 180 = 0
Use the quadratic formula
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
RELATED QUESTIONS
Hi, I could really use some help with this problem: during the first part of the trip,... (answered by stanbon,richwmiller)

Please help me with this problem? I have tried several solutions and keep getting stuck! (answered by rwm)

During the first part of a trip a canoeist travels 95 miles at a certain speed. The... (answered by mananth)

During the first part of a trip, a canoeist travels 35 miles at a certain speed. The... (answered by scott8148,stanbon)

During the first part of a trip, a canoeist travels 48 miles at a certain speed. The... (answered by mananth)

During the first part of a trip, a canoeist travels 45 miles at a certain speed. The... (answered by ankor@dixie-net.com)

Hi, I am completely lost. I need help with these please. 1) During the first part of... (answered by ewatrrr)

during the first part of a trip a canoeist travels 24 miles at a certain speed. The... (answered by TimothyLamb)

I need help, I have tried this question several times and still am not getting it right. (answered by josmiceli,mananth)