document.write( "Question 771446: Running at an average rate of 6 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 2 meters per second. The total time for the sprint and the jog back was 2 minutes 24 seconds. Find the length of the track. \n" ); document.write( "

Algebra.Com's Answer #470218 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+d+\"$ = the length of the track in meters
\n" ); document.write( "Let $\"+t+\"$ = the time spent sprinting in seconds
\n" ); document.write( "Convert minutes to seconds:
\n" ); document.write( " $\"+2%2A60+=+120+\"$ sec
\n" ); document.write( " $\"+120+%2B+24+=+144+\"$ sec
\n" ); document.write( " $\"+144+-+t+\"$ = time spent jogging in seconds
\n" ); document.write( "-----------------------------
\n" ); document.write( "Equation for sprinting:
\n" ); document.write( "(1) $\"+d+=+6t+\"$
\n" ); document.write( "Equation for jogging:
\n" ); document.write( "(2) $\"+d+=+2%2A%28+144+-+t+%29+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "(2) $\"+d+=+288+-+2t+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( "(2) $\"+6t+=+288+-+2t+\"$
\n" ); document.write( "(2) $\"+8t+=+288+\"$
\n" ); document.write( "(2) $\"+t+=+36+\"$ sec
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+d+=+6t+\"$
\n" ); document.write( "(1) $\"+d+=+6%2A36+\"$
\n" ); document.write( "(1) $\"+d+=+216+\"$
\n" ); document.write( "The track is 216 meters long
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+d+=+2%2A%28+144+-+t+%29+\"$
\n" ); document.write( "(2) $\"+216+=+2%2A%28+144+-+36+%29+\"$
\n" ); document.write( "(2) $\"+216+=+2%2A108+\"$
\n" ); document.write( "(2) $\"+216+=+216+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

\n" );