SOLUTION: During the first part of a trip, a canoeist travels 87 miles at a certain speed. The canoeist travels 9 miles on the second part of the trip at a speed 5 mph slower. The total time

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: During the first part of a trip, a canoeist travels 87 miles at a certain speed. The canoeist travels 9 miles on the second part of the trip at a speed 5 mph slower. The total time      Log On


   

Question 328753: During the first part of a trip, a canoeist travels 87 miles at a certain speed. The canoeist travels 9 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 the FIRST part of the trip? What was the speed on the SECOND part of the trip?
(type an integer or a decimal. 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 87 miles at a certain speed.
The canoeist travels 9 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 the FIRST part of the trip?
What was the speed on the SECOND part of the trip?
(type an integer or a decimal. Round to the nearest hundredth)
:
Let s = "a certain speed on the first part of the speed"
then
(s-5) = "speed on the second part of the trip"
:
:
Write a time equation: Time = dist/speed
:
1st part time + 2nd part time = 5 hrs
87%2Fs + 9%2F%28%28s-5%29%29 = 5
:
Multiply equation by s(s-5), results:
87(s-5) + 9s = 5s(s-5)
:
87s - 435 + 9s = 5s^2 - 25s
:
96s - 435 = 5s^2 - 25s
Arrange as a quadratic equation
5s^2 - 25s - 96s + 435 = 0
:
5s^2 - 121s + 435 = 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=-121; c= 435
s+=+%28-%28-121%29+%2B-+sqrt%28-121%5E2-4%2A5%2A435+%29%29%2F%282%2A5%29+
:
s+=+%28121+%2B-+sqrt%2814641+-+8700+%29%29%2F10+
:
s+=+%28121+%2B-+sqrt%285941+%29%29%2F10+
Two solutions, but this is the one that makes sense
s+=+%28121+%2B+77.08%29%2F10+
s = 198.08%2F10
s = 19.81 mph on the first part of the trip
then
19.81 - 5 = 14.81 mph on the 2nd part
:
:
Check solution
87%2F19.81 + 9%2F14.81 =
4.39 + .61 = 5 hrs, confirms our solutions