SOLUTION: During the first part of a trip, a canoeist travels 34 miles at a certain speed. The canoeist travels 9 miles on the second part of the trip at a speed 5mph slower. The total tim

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: During the first part of a trip, a canoeist travels 34 miles at a certain speed. The canoeist travels 9 miles on the second part of the trip at a speed 5mph slower. The total tim      Log On


   

Question 560125: During the first part of a trip, a canoeist travels 34 miles at a certain speed. The canoeist travels 9 miles on the second part of the trip at a speed 5mph slower. The total time for the trip is 5hrs. What was the speed on each part of the trip? Type an integer or decimal and round to the nearest hundredth.
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 34 miles at a certain speed.
The canoeist travels 9 miles on the second part of the trip at a speed 5mph slower.
The total time for the trip is 5hrs. What was the speed on each part of the trip?
:
Let s = the speed on the 1st 34 mi
then
(s-5) = speed on the last 9 mi
:
Write a time equation, time = dist/speed
:
fast time + slow time = 5 hrs
34%2Fs + 9%2F%28%28s-5%29%29 = 5
multiply by s(s-5), results:
34(s-5) + 9s = 5s(s-5)
34s - 170 + 9s = 5s^2 - 25s
43s - 170 = 5s^2 - 25s
0 = 5s^2 - 25s - 43s + 170
A quadratic equation\
5s^2 - 68s + 170 = 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 x=s; a=5; b=-68; c=170
s+=+%28-%28-68%29+%2B-+sqrt%28-68%5E2-4%2A5%2A170+%29%29%2F%282%2A5%29+
:
x+=+%2868+%2B-+sqrt%284624-3400+%29%29%2F10+
:
I'll let you do the rest of the math here
you will get two positive solutions, but only one will make sense
Check it in the original time equation