SOLUTION: A woman cycles 8ml/hr faster than she runs. Every morning she cycles 4 ml and runs 2.5 miles, for a total of one hour of exercise. How fast does she run?

Question 411382: A woman cycles 8ml/hr faster than she runs. Every morning she cycles 4 ml and runs 2.5 miles, for a total of one hour of exercise. How fast does she run?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A woman cycles 8ml/hr faster than she runs. Every morning she cycles 4 ml and runs 2.5 miles, for a total of one hour of exercise. How fast does she run?
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Running DATA:
rate = x mph ; distance = 2.5 miles ; time = d/r = 2.5/x hrs
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Cycle DATA:
rate = x+8 mph ; distance = 4 miles ; time = d/r = 4/(x+8) hrs
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Equation:
time + time = 1 hr
2.5/x + 4/(x+8) = 1 hr
2.5(x+8) + 4x = x(x+8)
6.5x + 20 = x^2+8x
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x^2+1.5x-20 = 0
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x = [-1.5 +- sqrt((1.5)^2-4*-20]/2
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x = [-1.5 +- sqrt(81.52)]/2
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Positive solution:
x = (-1.5+9.03)/2
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x = 7.5 mph (run rate)
x+8 = 15.5 mph (cycling rate)
==============================
Cheers,
Stan H.
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