Question 149484
A boy rides a bike 8 miles. The trip would have taken 20 minutes less if he had ridden 2 miles per hour faster. find his actual speed.
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Original DATA:
distance = 8 miles ; rate = x mph ; time = d/r = 8/x hrs
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Modified DATA:
distance = 8 miles ; rate = (x+2) mph ; time = d/r = 8/(x+2)
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EQUATION:
old time - new time = 20/60 = 1/3 hr
8/x + 8/(x+2) = 1/3
Multiply thru by 3x(x+2)
24(x+2) + 24x = x(x+2)
48x + 48 = x^2 + 2x
x^2 - 46x - 48 = 0
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x = [46 +- sqrt(46^2 -4*1*-48)]/2
Positive solution:
x = [46 + sqrt(2300)]/2
x = 47.02.. mph (actual speed)
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Cheers,
Stan H.