document.write( "Question 1024657: One hour after a hiker left a camp, a cyclist set out to catch up. If the hiker traveled 3 miles per hour and the cyclist travelled 6 miles per hour faster, how long will it take the cyclist to catch up with the hiker? \n" ); document.write( "

Algebra.Com's Answer #640075 by josmiceli(19441) $\"\"$ $\"About$

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The hiker had a head start of
\n" ); document.write( " $\"+d%5B1%5D+=+3%2A1+\"$
\n" ); document.write( " $\"+d%5B1%5D+=+3+\"$ mi
\n" ); document.write( "---------------
\n" ); document.write( "Start a stop watch when the cyclist leaves
\n" ); document.write( "Let $\"+t+\"$ = the time in hrs on the stop watch
\n" ); document.write( "when the cyclist catches up with the hiker
\n" ); document.write( "---------------
\n" ); document.write( "Let $\"+d+\"$ = distance cyclist traveled until
\n" ); document.write( "cyclist caught up with hiker
\n" ); document.write( "---------------
\n" ); document.write( "Hiker's equation:
\n" ); document.write( "(1) $\"+d+-+3+=+3t+\"$
\n" ); document.write( "Cyclist's equation:
\n" ); document.write( "(2) $\"+d+=+6t+\"$
\n" ); document.write( "----------------
\n" ); document.write( "Substitute (2) into (1)
\n" ); document.write( "(1) $\"+6t+-+3+=+3t+\"$
\n" ); document.write( "(1) $\"+3t+=+3+\"$
\n" ); document.write( "(1) $\"+t+=+1+\"$
\n" ); document.write( "The cyclist takes 1 hr to catch up with hiker
\n" ); document.write( "-----------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+d+=+6t+\"$
\n" ); document.write( "(2) $\"+d+=+6%2A1+\"$
\n" ); document.write( "(2) $\"+d+=+6+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+d+-+3+=+3t+\"$
\n" ); document.write( "(1) $\"+d+-+3+=+3%2A1+\"$
\n" ); document.write( "(1) $\"+d+-+3+=+3+\"$
\n" ); document.write( "(1) $\"+d+=+6+\"$
\n" ); document.write( "OK \n" ); document.write( "

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