document.write( "Question 624149: Howard lives 2 miles from school. When he rode his bicycle, he traveled 5 miles per hour faster than when he walked, and thus saved 25 minutes. What was his average rate of walking? \n" ); document.write( "

Algebra.Com's Answer #392647 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Howard lives 2 miles from school.
\n" ); document.write( " When he rode his bicycle, he traveled 5 miles per hour faster than when he walked, and thus saved 25 minutes.
\n" ); document.write( " What was his average rate of walking?
\n" ); document.write( ":
\n" ); document.write( "Let w = his av rate of walking
\n" ); document.write( "then
\n" ); document.write( "(w+5) = his av rate of riding
\n" ); document.write( ":
\n" ); document.write( "Since we are using mph, convert 25 min: 25/60 = 5/12 hrs
\n" ); document.write( ":
\n" ); document.write( "Write time equation; time = dist/speed
\n" ); document.write( ":
\n" ); document.write( " $\"2%2Fw\"$ - $\"2%2F%28%28w%2B5%29%29\"$ = $\"5%2F12\"$
\n" ); document.write( "multiply by 12w(w+5) to clear the denominator, results:
\n" ); document.write( "12(w+5)*2 - 12w(2) = 5w(w+5)
\n" ); document.write( ":
\n" ); document.write( "24w + 120 - 24w = 5w^2 + 25w
\n" ); document.write( "A quadratic equation
\n" ); document.write( "0 = 5w^2 + 25w - 120
\n" ); document.write( "Simplify, divide by 5
\n" ); document.write( "w^2 + 5w - 24 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(w+8)(w-3) = 0
\n" ); document.write( "the positive solution
\n" ); document.write( "w = 3 mph is the walking speed
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check this out (8 mph is the biking speed)
\n" ); document.write( "2/3 - 2/8 =
\n" ); document.write( "8/12 - 3/12 = 5/12 which is 25 min
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