document.write( "Question 945183: two persons are to run a race, but one can run 8 meters per second, whereas the other can run 2 meters per second. If the slower runner has a 81 meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time. \n" ); document.write( "

Algebra.Com's Answer #576354 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+d+\"$ = the distance in meters the faster runner travels
\n" ); document.write( "until the slower runner is caught
\n" ); document.write( "Let $\"+t+\"$ = time in seconds for faster runner to
\n" ); document.write( "catch slower runner
\n" ); document.write( "-----------------------
\n" ); document.write( "faster runner's equation:
\n" ); document.write( " $\"+d+=+8t+\"$
\n" ); document.write( "slower runner's equation:
\n" ); document.write( " $\"+d+-+81+=+2t+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+8t+-+81+=+2t+\"$
\n" ); document.write( " $\"+6t+=+81+\"$
\n" ); document.write( " $\"+t+=+13.5+\"$
\n" ); document.write( "In 13.5 seconds the faster runner catches
\n" ); document.write( "the slower runner
\n" ); document.write( " \n" ); document.write( "

\n" );