document.write( "Question 323778: David and Keith are route drivers for a fast -photo company. David route is 80 miles, and Keith’s is 100 miles. Keith averages 10 mph more than David and finishes his route 10 minutes before David. What is David’s speed. \n" ); document.write( "
Algebra.Com's Answer #231740 by josmiceli(19441)\"\" \"About 
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Equation for David:
\n" ); document.write( "\"d+=+r%2At\"
\n" ); document.write( "\"80+=+r%2At\"
\n" ); document.write( "Equation for Keith:
\n" ); document.write( "\"100+=+%28r+%2B+10%29%2A%28t+-+1%2F6%29\"
\n" ); document.write( "\"100+=+rt+%2B+10t+-+%281%2F6%29%2Ar+-+10%2F6\"
\n" ); document.write( "By substitution:
\n" ); document.write( "\"100+=+80+%2B+10t+-+%281%2F6%29%2A%2880%2Ft%29+-+10%2F6\"
\n" ); document.write( "\"20+=+10t+-+%2840%2F%283t%29+-+5%2F3%29\"
\n" ); document.write( "Multiply both sides by \"3t\"
\n" ); document.write( "\"60t+=+30t%5E2+-+40+-+5t\"
\n" ); document.write( "\"30t%5E2+-+65t+-+40+=+0\"
\n" ); document.write( "\"6t%5E2+-+13t+-+8+=+0\"
\n" ); document.write( "Use the quadratic formula
\n" ); document.write( "\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "\"a+=+6\"
\n" ); document.write( "\"b+=+-13\"
\n" ); document.write( "\"c+=+-8\"
\n" ); document.write( "\"t+=+%28-%28-13%29+%2B-+sqrt%28+%28-13%29%5E2-4%2A6%2A%28-8%29+%29%29%2F%282%2A6%29+\"
\n" ); document.write( "\"t+=+%28+13+%2B-+sqrt%28++169+%2B+192+%29%29%2F12+\"
\n" ); document.write( "\"t+=+%28+13+%2B-+sqrt%28++361+%29%29%2F12+\"
\n" ); document.write( "\"t+=+%28+13+%2B-+19%29%2F12+\"
\n" ); document.write( "\"t+=+32%2F12\"
\n" ); document.write( "\"t+=+8%2F3\"
\n" ); document.write( "For David:
\n" ); document.write( "\"80+=+r%2At\"
\n" ); document.write( "\"r+=+80%2F%288%2F3%29\"
\n" ); document.write( "\"r+=+240%2F8\"
\n" ); document.write( "\"r+=+30\"
\n" ); document.write( "David's speed is 30 mi/hr
\n" ); document.write( "check:
\n" ); document.write( "For Keith
\n" ); document.write( "\"100+=+%28r+%2B+10%29%2A%28t+-+1%2F6%29\"
\n" ); document.write( "\"100+=+%2830+%2B+10%29%2A%288%2F3+-+1%2F6%29\"
\n" ); document.write( "\"100+=+40%2A%2816%2F6+-+1%2F6%29\"
\n" ); document.write( "\"100+=+40%2A%2815%2F6%29\"
\n" ); document.write( "\"600+=+40%2A15\"
\n" ); document.write( "\"600+=+600\"
\n" ); document.write( "OK
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