SOLUTION: During the first part of a trip a canoeist travels 45 miles at a certain speed. The canoeist travels 12 miles on the second part of the trip at a speed 5 mph slower. The total time

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Question 468796: During the first part of a trip a canoeist travels 45 miles at a certain speed. The canoeist travels 12 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 4 hrs. What was the total time on each 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 45 miles at a certain speed.
The canoeist travels 12 miles on the second part of the trip at a speed 5 mph slower.
The total time for the trip is 4 hrs.
What was the total time on each trip?
:
Let s = speed for the 1st 45 mi
then
(s-5) = speed for the last 12 mi
:
Write a time equation, time = dist/speed
:
1st part time + 2nd part time = 4 hr
45%2Fs + 12%2F%28%28s-5%29%29 = 4
multiply by s(s-5), results:
45(s-5) + 12s = 4s(s-5)
:
45s - 225 + 12s = 4s^2 - 20s
57s - 225 = 4s^2 - 20s
Arrange as a quadratic on the right
0 = 4s^2 - 20s - 57s + 225
:
4s^2 - 77s + 225 = 0
Solve this with the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem we have:
s+=+%28-%28-77%29+%2B-+sqrt%28-77%5E2-4%2A4%2A225+%29%29%2F%282%2A4%29+
Do the math, only one solution will make sense