SOLUTION: 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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-> SOLUTION: 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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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. Found 3 solutions by nerdybill, stanbon, mangopeeler07:Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! 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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20 minutes = 20/60 hours = 1/3 hour
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Let x = actual speed
and y = actual time taken
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xy = 8 (equation 1)
(x+2)(y-1/3) = 8 (equation 2)
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solving equation 1 for y:
xy = 8
y = 8/x
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substitute the above into equation 2 and solve for x:
(x+2)(y-1/3) = 8
(x+2)(8/x-1/3) = 8
multiply both sides by 3x:
(x+2)(24-x) = 24x
24x + 48 - x^2 - 2x = 24x
22x + 48 - x^2= 24x
0 = x^2 + 2x - 48
0 = (x+8)(x-6)
x = {-8, 6}
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Since speed can't be negative, it must be the positive solution.
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x = 6 mph
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You can put this solution on YOUR website! 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.
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