SOLUTION: Hi, I'm not even sure how to start to set this problem up. :/ Thanks for your help!! Dirk and Garret decide to have a 40-mile bike race. During the race, Dirk averages 2 mile

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Question 608561: Hi,
I'm not even sure how to start to set this problem up. :/ Thanks for your help!!
Dirk and Garret decide to have a 40-mile bike race. During the race, Dirk averages 2 miles per hour faster than Garret and beats Garret by 2/3 of an hour. What was each man's speed?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Dirk and Garret decide to have a 40-mile bike race. During the race, Dirk averages 2 miles per hour faster than Garret and beats Garret by 2/3 of an hour. What was each man's speed?
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Dirk DATA:
distance = 40 miles ; rate = x+2 mph ; time = 40/(x+2) hrs
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Garret DATA:
distance = 40 miles; rate = x mph ; time = 40/x hrs
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Equation:
Garret time - Dirk time = (2/3)hr.
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40/x - 40/(x+2) = 2/3
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Multiply thru by 3x(x+2) to get:
40*3*(x+2) - 40*3*x = x(x+2)
120x + 240 - 120x = x^2 + 2x
---
x^2 +2x - 240 = 0
Use the Quadratic Formula to find x = 14.52 mph (Garret's rate)
and x + 2 = 16.52 mph (Dirk's rate)
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Cheers,
Stan H.