document.write( "Question 230087: A freight train leaves a station traveling 60 miles per hour. Thirty minutes later a passenger train leaves the station in the same direction on a parallel track at a speed of 72 miles per hour. How long will it take the passenger train to catch the freight train? \n" ); document.write( "

Algebra.Com's Answer #170448 by josmiceli(19441) $\"\"$ $\"About$

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In 30 min, the freight train has gone:
\n" ); document.write( " $\"d+=+60%2A%281%2F2%29\"$ mi
\n" ); document.write( " $\"d+=+30\"$ mi (it's headstart)
\n" ); document.write( "When the passenger train leaves the station, I start a stopwatch
\n" ); document.write( "and I'll stop it at time = $\"t\"$ when trains meet
\n" ); document.write( "Let $\"d%5Bp%5D\"$ = distance the passenger train has to
\n" ); document.write( "go to catch freight train
\n" ); document.write( "For passenger train:
\n" ); document.write( "(1) $\"d%5Bp%5D+=+72t\"$
\n" ); document.write( "For freight train:
\n" ); document.write( "(2) $\"d%5Bp%5D+-+30+=+60t\"$
\n" ); document.write( "Substitute (1) in (2)
\n" ); document.write( " $\"72t+-+30+=+60t\"$
\n" ); document.write( " $\"12t+=+30\"$
\n" ); document.write( " $\"t+=+5%2F2\"$
\n" ); document.write( "The passenger train catches the freight train in 2.5 hrs
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"d%5Bp%5D+=+72t\"$
\n" ); document.write( " $\"d%5Bp%5D+=+72%2A2.5\"$
\n" ); document.write( " $\"d%5Bp%5D+=+180\"$ mi
\n" ); document.write( "and
\n" ); document.write( "(2) $\"d%5Bp%5D+-+30+=+60t\"$
\n" ); document.write( " $\"d%5Bp%5D+=+60%2A2.5+%2B+30\"$
\n" ); document.write( " $\"d%5Bp%5D+=+150+%2B+30\"$
\n" ); document.write( " $\"d%5Bp%5D+=+180\"$ mi
\n" ); document.write( "OK \n" ); document.write( "

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