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
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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) (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
+ = 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:
in this problem: x=s; a=5; b=-121; c= 435
:
:
Two solutions, but this is the one that makes sense
s =
s = 19.81 mph on the first part of the trip
then
19.81 - 5 = 14.81 mph on the 2nd part
:
:
Check solution
+ =
4.39 + .61 = 5 hrs, confirms our solutions
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