document.write( "Question 182489: at noon a train leaves washington d.c headed for charleston south carolina a distance of 500 mi. the train travels at a speed of 60 mph. at 1 p.m. a second train leaves charleston headed for washington d.c. traveling at 50 mph. how long after the train leaves charleston will the two trains pass each other \n" ); document.write( "
Algebra.Com's Answer #137003 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
For 1st train:
\n" ); document.write( "(a) \"d%5B1%5D+=+r%5B1%5D%2At%5B1%5D\"
\n" ); document.write( "For 2nd train:
\n" ); document.write( "(b) \"d%5B2%5D+=+r%5B2%5D%2At%5B2%5D\"
\n" ); document.write( "given:
\n" ); document.write( "(c) \"d%5B1%5D+%2B+d%5B2%5D+=+500\" mi
\n" ); document.write( "(d) \"r%5B1%5D+=+60\" mi/hr
\n" ); document.write( "(e) \"r%5B2%5D+=+50\" mi/hr
\n" ); document.write( "(f) \"t%5B2%5D+=+t%5B1%5D+-+1\" hrs
\n" ); document.write( "-------------------------
\n" ); document.write( "Subtract \"d%5B1%5D\" from both sides of (c),
\n" ); document.write( "\"d%5B2%5D+=+500+-+d%5B1%5D\"
\n" ); document.write( "Now rewrite (a) and (b)
\n" ); document.write( "For 1st train:
\n" ); document.write( "(a) \"d%5B1%5D+=+60%2At%5B1%5D\"
\n" ); document.write( "For 2nd train:
\n" ); document.write( "(b) \"500+-+d%5B1%5D+=+50%2A%28t%5B1%5D+-+1%29\"
\n" ); document.write( "I have 2 equations and 2 unknowns, so it's solvable
\n" ); document.write( "(b) \"500+-+d%5B1%5D+=+50%2A%28t%5B1%5D+-+1%29\"
\n" ); document.write( "(b) \"-d%5B1%5D+=+50t%5B1%5D+-+50+-+500\"
\n" ); document.write( "(b) \"-d%5B1%5D+=+50t%5B1%5D+-+550\"
\n" ); document.write( "Now add (a) and (b)
\n" ); document.write( "(a) \"d%5B1%5D+=+60%2At%5B1%5D\"
\n" ); document.write( "(b) \"-d%5B1%5D+=+50t%5B1%5D+-+550\"
\n" ); document.write( "\"0+=+60t%5B1%5D+%2B+50t%5B1%5D+-+550\"
\n" ); document.write( "\"110t%5B1%5D+=+550\"
\n" ); document.write( "\"t%5B1%5D+=+5\" hrs
\n" ); document.write( "This is the time it took the DC to Charlston train to meet the other
\n" ); document.write( "The problem wants the time for the Charlston to DC train
\n" ); document.write( "\"t%5B2%5D+=+t%5B1%5D+-+1\"
\n" ); document.write( "\"t%5B2%5D+=+5+-+1\"
\n" ); document.write( "\"t%5B2%5D+=+4\" hrs answer
\n" ); document.write( "check answer:
\n" ); document.write( "(a) \"d%5B1%5D+=+r%5B1%5D%2At%5B1%5D\"
\n" ); document.write( "(a) \"d%5B1%5D+=+60%2A5\"
\n" ); document.write( "(a) \"d%5B1%5D+=+300\"
\n" ); document.write( "and
\n" ); document.write( "(b) \"d%5B2%5D+=+r%5B2%5D%2At%5B2%5D\"
\n" ); document.write( "(b) \"d%5B2%5D+=+50%2A4\"
\n" ); document.write( "(b) \"d%5B2%5D+=+200\"
\n" ); document.write( "(c) \"d%5B1%5D+%2B+d%5B2%5D+=+500\" mi
\n" ); document.write( "(c) \"300+%2B+200+=+500\"
\n" ); document.write( "OK
\n" ); document.write( "
\n" );