SOLUTION: During the first part of a trip, a canoeist travels 71 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 tim

Algebra ->  Radicals -> SOLUTION: During the first part of a trip, a canoeist travels 71 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 tim      Log On


   

Question 376588: During the first part of a trip, a canoeist travels 71 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 5 hours. 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 71 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 5 hours. What was the speed on EACH part of the trip?
:
Let s = speed for the 1st part of the trip
then
(s-5) = speed on the 2nd part of the trip
:
Write time equation; time = dist/speed
:
1st speed time + 2nd speed time = 5 hrs
71%2Fs + 12%2F%28%28s-5%29%29 = 5
Multiply by s(s-5) to clear the denominators, results:
71(s-5) + 12s = 5s(s-5)
71s - 355 + 12s = 5s^2 - 25s
83s - 355 = 5s^2 - 25s
0 = 5s^2 - 25s - 83s + 355
5s^2 - 108s + 355 = 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+
Where x = s; a=5; b=-108; c=355
s+=+%28-%28-108%29+%2B-+sqrt%28-108%5E2-4%2A5%2A355+%29%29%2F%282%2A5%29+
:
s+=+%28108+%2B-+sqrt%2811664-7100+%29%29%2F10+
:
s+=+%28108+%2B-+sqrt%284564+%29%29%2F10+
two solutions
s+=+%28108+%2B+67.557%29%2F10+
s = 175.557%2F10
s = 17.5557
and
s+=+%28108+-+67.557%29%2F10+
s = 40.443%2F10
s = 4.0443
:
s = 17.5557 mph is the only reasonable speed for the 1st part of the trip
and
17.5557 - 5 = 12.5557 mph is the speed on the 2nd part of the trip
:
:
See if this is true, find the time at each speed
71/17.5557 = 4.044 hrs
12/12.5557 = .9557
-------------------
total time: 4.9997 ~ 5 hrs