SOLUTION: During the first part of a trip, a canoeist travels 37 miles at a certain speed. The canoeist travels 7 miles on the second part or the trip at a speed 5 mph slower. The total time

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Question 169481: During the first part of a trip, a canoeist travels 37 miles at a certain speed. The canoeist travels 7 miles on the second part or the trip at a speed 5 mph slower. The total time for the trip is 4 hours. What is the speed on each part of the trip?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
During the first part of a trip, a canoeist travels 37 miles at a certain speed.
The canoeist travels 7 miles on the second part or the trip at a speed 5 mph
slower. The total time for the trip is 4 hours. What is the speed on each part
of the trip?
:
Let s = speed on the 1st part of the trip
then
(s-5) = speed on the 2nd part
:
Write a time equation: Time = dist%2Fspeed
:
1st part time + 2nd part time = 4 hrs
37%2Fs + 7%2F%28%28s-5%29%29 = 4
:
Multiply equation by s(s-5) to get rid of the denominators, results:
37(s-5) = 7s = 4s(s-5)
:
37s - 185 + 7s = 4s^2 - 20s
:
44s - 185 = 4s^2 - 20s
:
Arrange as a quadratic equation
4s^2 - 20s - 44s + 185 = 0
:
4s^2 - 64s + 185 = 0
:
Use the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem x=s; a=4; b=-64; c=185
s+=+%28-%28-64%29+%2B-+sqrt%28-64%5E2+-+4%2A4%2A185+%29%29%2F%282%2A4%29+
:
s+=+%2864+%2B-+sqrt%284096+-+2960%29%29%2F%288%29+
:
I'll let you do the math. You will get two positive solutions, but only one will make sense.
Check your solution by substituting for s in the original equation.