SOLUTION: During the first part of a trip, a canoeist travels 45 miles at a certain speed. The canoeist travels 20 miles on the second part of the trip at a speed 5 mph slower. The total tim

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: During the first part of a trip, a canoeist travels 45 miles at a certain speed. The canoeist travels 20 miles on the second part of the trip at a speed 5 mph slower. The total tim      Log On


   

Question 600979: During the first part of a trip, a canoeist travels 45 miles at a certain speed. The canoeist travels 20 miles on the 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?
The speed on the first part of the trip was _______ mph.
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 20 miles on the 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?
:
Let s = speed the first part of the trip
and
(s-5) = speed on the 2nd part
:
Write a time equation: time = dist/speed
:
1st part time + 2nd part time = 2 hrs
45%2Fs + 20%2F%28%28s-5%29%29 = 2
multiply by s(s-5) to clear the denominators, results:
45(s-5) + 20s = 2s(s-5)
:
45s - 225 + 20s = 2s^2 - 10s
:
65s - 225 = 2s^2 - 10s
:
0 = 2s^2 - 10s - 65s + 225
A quadratic equation
2s^2 - 75s + 225 = 0
Use the quadratic formula to fins s
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation: x=s; a=2; b=-75; c=225
s+=+%28-%28-75%29+%2B-+sqrt%28-75%5E2-4%2A2%2A225+%29%29%2F%282%2A2%29+
:
s+=+%2875+%2B-+sqrt%285625-1800+%29%29%2F4+
:
s+=+%2875+%2B-+sqrt%283825+%29%29%2F4+
Two solutions, but only this one makes sense.
s+=+%2875+%2B+61.85%29%2F4+
s = 136.84%2F4
s = 34.2 mph on the 1st part of the trip
and
34.2 - 5 = 29.2 mph on the 2nd part
:
:
Let's see if this checks out, find sum of the times at each speed
45/34.2 = 1.3158 hrs at 34.2 mph
20/29.2 = 0.6849 hrs at 29.2 mph
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tot time: 2.0007 hrs which is the total time