document.write( "Question 1139188: Evan went on a bike ride of 120 miles. He realized that if he had gone 18 mph faster, he would have arrived 15 hours sooner. How fast did he actually ride?
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Algebra.Com's Answer #756966 by greenestamps(13215) $\"\"$ $\"About$

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\n" ); document.write( "An algebraic solution....

\n" ); document.write( "let x be the speed he rode at
\n" ); document.write( "Then x+18 is the speed he could have ridden at

\n" ); document.write( "The times to go 120 miles at the two speeds are 120/x and 120/(x+18).

\n" ); document.write( "The problem says the time would be 15 hours less at the higher speed:

\n" ); document.write( " $\"120%2Fx-120%2F%28x%2B18%29+=+15\"$
\n" ); document.write( " $\"120%28x%2B18%29-120x+=+15x%28x%2B18%29\"$
\n" ); document.write( " $\"8%28x%2B18%29-8x+=+x%28x%2B18%29\"$
\n" ); document.write( " $\"144+=+x%5E2%2B18x\"$
\n" ); document.write( " $\"x%5E2%2B18x-144+=+0\"$
\n" ); document.write( " $\"x%2B24%29%28x-6%29+=+0\"$
\n" ); document.write( "x = -24 (nonsense) or x = 6

\n" ); document.write( "His actual speed was 6mph. (A very slow bicycle speed!)

\n" ); document.write( "CHECK:
\n" ); document.write( "120/6 = 20
\n" ); document.write( "120/(6+18) = 120/24 = 5
\n" ); document.write( "20-5 = 15

\n" ); document.write( "An informal solution -- if algebra is not required....

\n" ); document.write( "Make a list of pairs of numbers whose product is 120 and find two pairs that meet the conditions of the problem.

\n" ); document.write( "1*120
\n" ); document.write( "2*60
\n" ); document.write( "3*40
\n" ); document.write( "4*30
\n" ); document.write( "5*24
\n" ); document.write( "6*20
\n" ); document.write( "8*15
\n" ); document.write( "10*12

\n" ); document.write( "The pairs 5*24 and 6*20 satisfy the given conditions: 6+18 = 24; 20-5 = 15. \n" ); document.write( "

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