SOLUTION: Suppose that a cyclist began a 234 mile ride across the state at the western edge of the state at the same time that a car traveling toward it leaves the eastern end of the state

Question 1036797: Suppose that a cyclist began a 234 mile ride across the state at the western edge of the state at the same time that a car traveling toward it leaves the eastern end of the state. If the bicycle in car met after 4 1/2 hours and the car travel 31.2 mph faster than the bicycle find the average rate of each?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose that a cyclist began a 234 mile ride across the state at the western edge of the state at the same time that a car traveling toward it leaves the eastern end of the state. If the bdicycle in car met after 4 1/2 hours and the car travel 31.2 mph faster than the bicycle find the average rate of each?
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cyclist DATA:
distance = d miles ; rate = r mph ; time = d/r hours
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car DATA:
dist = 234-d miles ; rate = r + 31.2 mph ; time = (234-d)/(31.2+r) hours
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Equation:
(234-d)/(31.2+r) = d/r
d/r = 4.5
d= 4.5r
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31.2d + rd = 234r-rd
2rd = 234r - 31.2d
2r(4.5r) = 234r - 31.2(4.5r)
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9r^2 = 93.6r
r(9r-93.6) = 0
r = 10.4 (bike rate)
r+31.2 = 41.6 mph (car rate)
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Cheers,
Stan H.
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