document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #109672 by nerdybill(7384) $\"\"$ $\"About$

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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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\n" ); document.write( "20 minutes = 20/60 hours = 1/3 hour
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\n" ); document.write( "Let x = actual speed
\n" ); document.write( "and y = actual time taken
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\n" ); document.write( "xy = 8 (equation 1)
\n" ); document.write( "(x+2)(y-1/3) = 8 (equation 2)
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\n" ); document.write( "solving equation 1 for y:
\n" ); document.write( "xy = 8
\n" ); document.write( "y = 8/x
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\n" ); document.write( "substitute the above into equation 2 and solve for x:
\n" ); document.write( "(x+2)(y-1/3) = 8
\n" ); document.write( "(x+2)(8/x-1/3) = 8
\n" ); document.write( "multiply both sides by 3x:
\n" ); document.write( "(x+2)(24-x) = 24x
\n" ); document.write( "24x + 48 - x^2 - 2x = 24x
\n" ); document.write( "22x + 48 - x^2= 24x
\n" ); document.write( "0 = x^2 + 2x - 48
\n" ); document.write( "0 = (x+8)(x-6)
\n" ); document.write( "x = {-8, 6}
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\n" ); document.write( "Since speed can't be negative, it must be the positive solution.
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\n" ); document.write( "x = 6 mph
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