SOLUTION: During the first part of a trip a canoeist travels 95 miles at a certain speed. The canoeist travels 22 miles on the second part of the trip at a speed of 5 mph slower. The total t

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Question 473811: During the first part of a trip a canoeist travels 95 miles at a certain speed. The canoeist travels 22 miles on the second part of the trip at a speed of 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 95 miles at a certain speed.
The canoeist travels 22 miles on the second part of the trip at a speed of 5 mph slower.
The total time for the trip is 3 hrs. What was the speed on each part of the trip?
:
A totally unrealistic problem, a canoe that cover over 100 mi in 3 hrs!!
But anyway:
:
Let s = speed for the 1st part of 95 mi
then
(s-5) = speed for the 2nd part of 22 mi
:
Write a time equation, time = dist/speed
1st part time + 2nd part time = 3 hrs
95%2Fs + 22%2F%28%28s-5%29%29 = 3
multiply by s(s-5), resulting in:
95(s-5) + 22s = 3s(s-5)
:
95s - 475 + 22s = 3s^2 - 15s
117s - 475 = 3s^2 - 15s
0 = 3s^2 - 15s - 117s + 475
A quadratic equation
3s^2 - 132s + 475 = 0
use the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=3; b=-132; c=475
x+=+%28-%28-132%29+%2B-+sqrt%28132%5E2-4%2A3%2A475+%29%29%2F%282%2A3%29+
You do the math to find s, only one of the solutions will make sense