SOLUTION: I saw that your email address was attached to a Math Problem you solved at an earlier date on algebra.com. I was hoping you could help me with a problem I am having as well. Her

Question 569529:
I saw that your email address was attached to a Math Problem you solved at an earlier date on algebra.com. I was hoping you could help me with a problem I am having as well. Here is the problem, thank you in advance, if you cannot help me I understand :)

During the first part of a trip a canoeist travels 80 miles at a certain speed.
The canoeist travels 9 miles on the second part of the trip at a speed of 5 mph slower.
The total time for the trip is 4 hrs. What was the speed on each part of the trip?
Please provide exact answers for each part!
The speed on the first part of the trip was :__________ mph
The speed on the second part of the trip was:___________ mph
Simplify your answer. Type as integer or a decimal, round to the nearest hundredth

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
During the first part of a trip a canoeist travels 80 miles at a certain speed.
The canoeist travels 9 miles on the second part of the trip at a speed of 5 mph slower.
The total time for the trip is 4 hrs. What was the speed on each part of the trip?
--------------
1st Part DATA:
distance = 80 miles ; rate = x mph ; time = d/r = 80/x hrs
-----
2nd Part DATA:
distance 9 miles ; rate = x-5 mph ; time = d/r = 9/(x-5) hrs
-----------------
Equation:
time + time = 4 hrs
80/x + 9/(x-5) = 4 hrs
---
Multiply thru by x(x-5) to get:
80(x-5) + 9x = 4x(x-5)
89x - 400 = 4x^2 - 20x
------
4x^2-109x+400 = 0
Usable positive solution:
x = 22.88 mph
===================
Cheers,
Stan H.
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