document.write( "Question 942720: Maureen can run at a rate that is 2 miles per hour faster than her friend Hector's rate. While training for a mini marathon, Maureen gives Hector a half-hour head start and then begins chasing Hector on the same route. If Maureen passes Hector 12 miles from the starting point, how fast is each running?
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Algebra.Com's Answer #574718 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+s+\"$ = Hector's speed in mi/hr
\n" ); document.write( " $\"+s+%2B+2+\"$ = Maureen's speed in mi/hr
\n" ); document.write( "----------------
\n" ); document.write( "Hector's head start is:
\n" ); document.write( " $\"+d%5B1%5D+=+s%2A%281%2F2%29+\"$
\n" ); document.write( " $\"+d%5B1%5D+=+.5s+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "Start a stopwatch when Maureen leaves
\n" ); document.write( "Let $\"+t+\"$ = time in hrs on stopwatch
\n" ); document.write( "when she catches Hector
\n" ); document.write( "----------------------
\n" ); document.write( "Hector's equation:
\n" ); document.write( "(1) $\"+12+-+.5s+=+s%2At+\"$
\n" ); document.write( "Maureen's equation:
\n" ); document.write( "(2) $\"+12+=+%28+s%2B2+%29%2At+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "(1) $\"+s%2At+%2B+.5s+=+12+\"$
\n" ); document.write( "(1) $\"+s%2A%28+t+%2B+.5+%29+=+12+\"$
\n" ); document.write( "(1) $\"+s+=+12+%2F+%28+t+%2B+.5+%29+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "(2) $\"+12+=+s%2At+%2B+2t+\"$
\n" ); document.write( "(2) $\"+s%2At+=+12+-+2t+\"$
\n" ); document.write( "(2) $\"+s+=+%28+12+-+2t+%29+%2F+t+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+12%2F%28+t+%2B+.5+%29+=+%28+12+-+2t+%29+%2F+t+\"$
\n" ); document.write( " $\"+12t+=+%28+12+-+2t+%29%2A%28+.5+%2B+t+%29+\"$
\n" ); document.write( " $\"+12t+=+6+-+t+%2B+12t+-+2t%5E2+\"$
\n" ); document.write( " $\"+2t%5E2+%2B+t+-+6+=+0+\"$
\n" ); document.write( " $\"+%28+2t+-+3+%29%2A%28+t+%2B+2+%29+=+0+\"$ ( just a wild guess )
\n" ); document.write( " $\"+2t+=+3+\"$
\n" ); document.write( " $\"+t+=+1.5+\"$ ( can't have negative time )
\n" ); document.write( "(2) $\"+12+=+%28+s%2B2+%29%2At+\"$
\n" ); document.write( "(2) $\"+12+=+%28+s%2B2+%29%2A1.5+\"$
\n" ); document.write( "(2) $\"+12+=+1.5s+%2B+3+\"$
\n" ); document.write( "(2) $\"+1.5s+=+9+\"$
\n" ); document.write( "(2) $\"+s+=+6+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+s+%2B+2+=+8+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "Hector runs at 6 mi/hr
\n" ); document.write( "Maureen runs at 8 mi/hr
\n" ); document.write( "-----------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+12+-+.5s+=+s%2At+\"$
\n" ); document.write( "(1) $\"+12+-+.5%2A6+=+6%2A1.5+\"$
\n" ); document.write( "(1) $\"+12+-+3+=+9+\"$
\n" ); document.write( "(1) $\"+9+=+9+\"$
\n" ); document.write( "OK
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