document.write( "Question 723216: a freight train leaves a station and travels north at 60 mph. two hours later, a passenger train leaves on a parallel track and travels north at 100 mph. how long will it take the passenger train to overtake the frieght train? how far from the station will they meet \n" ); document.write( "

Algebra.Com's Answer #443075 by josmiceli(19441) $\"\"$ $\"About$

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In 2 hrs, the freight train gets a head start of
\n" ); document.write( " $\"+60%2A2+=+120+\"$ mi
\n" ); document.write( "Let $\"+d+\"$ = the distance the passenger train has to
\n" ); document.write( "travel to catch the freight train
\n" ); document.write( "-----------------
\n" ); document.write( "Start a stopwatch when the passenger train leaves
\n" ); document.write( "Let $\"+t+\"$ = the time on the stopwatch when they meet
\n" ); document.write( "------------------
\n" ); document.write( "Equation for freight train:
\n" ); document.write( " $\"+d+-+120+=+60t+\"$
\n" ); document.write( "Equation for passenger train:
\n" ); document.write( " $\"+d+=+100t+\"$
\n" ); document.write( "------------
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+100t+-+120+=+60t+\"$
\n" ); document.write( " $\"+40t+=+120+\"$
\n" ); document.write( " $\"+t+=+3+\"$ hrs
\n" ); document.write( "and
\n" ); document.write( " $\"+d+=+100t+\"$
\n" ); document.write( " $\"+d+=+100%2A3+\"$
\n" ); document.write( " $\"+d+=+300+\"$ mi
\n" ); document.write( "They will meet 300 mi from the station
\n" ); document.write( "check:
\n" ); document.write( " $\"+d+-+120+=+60t+\"$
\n" ); document.write( " $\"+300+-+120+=+60%2A3+\"$
\n" ); document.write( " $\"+180+=+180+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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