SOLUTION: Could someone please explain to me step by step how to complete this problem? I am able to get to the part where you simplify but am not able to get no farther. During the first p

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Question 526139: Could someone please explain to me step by step how to complete this problem? I am able to get to the part where you simplify but am not able to get no farther.
During the first part of a trip, a canoeist travels 91 miles at a certain speed. The canoeist travels 2 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 3 hrs. What was 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 61 miles at a certain speed.
The canoeist travels 2 miles on the second part of the trip at a speed 5 mph slower.
The total time for the trip is 3 hours. What was the speed on each part of the trip?
:
Let s = the speed for the 1st 61 mi
then
(s-5) = the speed for the last 2 mi
:
Write a time equation, time = dist/speed
:
faster time + slower time = 3 hrs
61%2Fs + 2%2F%28s-5%29 = 3
:
multiply by s(s-5), results:
61(s-5) + 2s = 3s(s-5)
:
61s - 305 + 2s = 3s^2 - 15s
63s - 305 = 3s^2 - 15s
Arrange as a quadratic equation on the right
0 = 3s^2 - 15s - 63s + 305
3s^2 - 78s + 305 = 0
Use the quadratic formula to find s:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this problem, a=3, b=-78, c=305, x=s
s+=+%28-%28-78%29+%2B-+sqrt%28-78%5E2-4%2A3%2A305+%29%29%2F%282%2A3%29+
:
s+=+%2878+%2B-+sqrt%286084-3660+%29%29%2F6+
:
s+=+%2878+%2B-+sqrt%282424%29%29%2F6+
Two solutions
s+=+%2878+%2B+49.234%29%2F6+
s = 127.234%2F6
s = 21.206
and
s+=+%2878+-+49.234%29%2F6+
s = 28.766%2F6
s = 4.794
:
Obviously the only reasonable solution:
s = 21.206 mph on the first 61 mi
and
16.206 mph on the last two miles
:
:
See if that check out, find the actual time of each
61/21.206 = 2.876 hrs
2/16.206 = .123 hrs
----------------------
total time: 3.0 hrs