document.write( "Question 250722: Zeke's motor cycle traveled 270 miles at a certain speed. Had he gone 15 mph faster, the trip would have taken 3 hours less. Find the speed of the motorcycle. \n" ); document.write( "
Algebra.Com's Answer #184781 by drk(1908)\"\" \"About 
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This is an RTD problem. Here is the table
\n" ); document.write( "vehicle . . . . . . . rate . . . . . . . . time . . . . . . . .distance
\n" ); document.write( "cycle . . . . . . . . . R . . . . . . .. . . 270/R . . . . . .. 270
\n" ); document.write( "cycle . . . . . . . . .R + 15 . .. . . . 270/R - 3 . . . .. 270\r
\n" ); document.write( "\n" ); document.write( "I let R = rate. The first time is D / R = 270 / R. All times are in hours, so the second time is
\n" ); document.write( "(270/R - 3) hours.
\n" ); document.write( "Look at the second line.
\n" ); document.write( "(R + 15)(270/R - 3) = 270
\n" ); document.write( "By FOIL, we get
\n" ); document.write( "270 - 3R + 4050/R - 45 = 270
\n" ); document.write( "multiply both sides by R. we get
\n" ); document.write( "270R - 3R^2 + 4050 - 45R = 270R.
\n" ); document.write( "Simplify to get
\n" ); document.write( "3R^2 + 45R - 4050 = 0
\n" ); document.write( "dividing by 3, we get
\n" ); document.write( "R^2 + 15R - 1350 = 0
\n" ); document.write( "factoring, we get
\n" ); document.write( "(R + 45)(R - 30) = 0
\n" ); document.write( "R = -45 or R = 30.
\n" ); document.write( "we can use -45, so
\n" ); document.write( "R = 30. The motorcycle was traveling at 30 mph. \n" ); document.write( "
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