document.write( "Question 82051: going skiing leon drove 270 miles to the lodge in the same time as pat drove 330 miles to the lodge. If pat drove 10 miles per hour faster than leon, then how fast did each of them drive.
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Algebra.Com's Answer #58807 by ptaylor(2198) $\"\"$ $\"About$

You can put this solution on YOUR website!
distance(d) equals rate(r) times time(t) or d=rt;t=d/r and r=d/t\r
\n" ); document.write( "\n" ); document.write( "Let r=Leon's rate of speed
\n" ); document.write( "then r+10=Pat's rate of speed\r
\n" ); document.write( "\n" ); document.write( "Time it took Leon to make the trip=d/r=270/r
\n" ); document.write( "Time it took Pat to make the trip=d/r=330/(r+10)\r
\n" ); document.write( "\n" ); document.write( "We are told that they both drove to the lodge in the same amount of time. So:\r
\n" ); document.write( "\n" ); document.write( "270/r=330/(r+10) multiply both sides by r(r+10) to get rid of the fractions (this is equivalent to cross multiplying)\r
\n" ); document.write( "\n" ); document.write( "270(r+10)=330r get rid of parens\r
\n" ); document.write( "\n" ); document.write( "270r+2700=330r subtract 270r from both sides\r
\n" ); document.write( "\n" ); document.write( "270r-270r+2700=330r-270r collect like terms\r
\n" ); document.write( "\n" ); document.write( "60r=2700 divide both sides by 60\r
\n" ); document.write( "\n" ); document.write( "r=45 mph-----------------------------------Leon's rate of speed\r
\n" ); document.write( "\n" ); document.write( "r+10=45+10=55 mph------------------------------Pat's rate of speed\r
\n" ); document.write( "\n" ); document.write( "CK\r
\n" ); document.write( "\n" ); document.write( "For Leon t=d/r; t=270/45=6 hrs
\n" ); document.write( "For Pat t=d/r; t=330/55=6 hrs\r
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\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor
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