document.write( "Question 792404: To travel 88 miles, it takes Sue, riding a moped, 4 hours less time than it takes Doreen to travel 56 miles riding a bicycle. Sue travels 15 miles per hour faster than Doreen. Find the times and rates of both girls. \n" ); document.write( "

Algebra.Com's Answer #479971 by mananth(16946) $\"\"$ $\"About$

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Doreen rate --------x mph----------------------56 miles
\n" ); document.write( "sue rate ------------x+15 mph------------------88 miles\r
\n" ); document.write( "\n" ); document.write( "t=d/r\r
\n" ); document.write( "\n" ); document.write( "Sue time - Doreen time = 4 hours\r
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\n" ); document.write( "\n" ); document.write( "56/x - 88/(x+15) =4\r
\n" ); document.write( "\n" ); document.write( "multiply by x(x+15)\r
\n" ); document.write( "\n" ); document.write( "56(x+15)-88x=4x(x+15)\r
\n" ); document.write( "\n" ); document.write( "56x+840-88x=4x^2+60x\r
\n" ); document.write( "\n" ); document.write( "-32x+840=4x^2+60x\r
\n" ); document.write( "\n" ); document.write( "4x^2+60x+32x-840=0\r
\n" ); document.write( "\n" ); document.write( "4x^2+92x-840=0\r
\n" ); document.write( "\n" ); document.write( "/4
\n" ); document.write( "x^2+23x-210=0\r
\n" ); document.write( "\n" ); document.write( "x^2+30x-7x-210=0\r
\n" ); document.write( "\n" ); document.write( "x(x+30)-7(x+30)=0\r
\n" ); document.write( "\n" ); document.write( "(x+30)(x-7)=0\r
\n" ); document.write( "\n" ); document.write( "x=-30 OR x=7\r
\n" ); document.write( "\n" ); document.write( "ignore negative\r
\n" ); document.write( "\n" ); document.write( "x= 7 speed of Doreen
\n" ); document.write( "7+15 = 22 mph speed of Sue\r
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