document.write( "Question 561656: two trains, each 400 ft long. run in parallel tracks. when running in the same direction, they completely passed each other in 20 seconds. when running in opposite direction, the completely passed each other in 5 seconds. find the rate of each train. kindly show the solution. thanks :) \n" ); document.write( "

Algebra.Com's Answer #364334 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
It's easier for me to think of one train
\n" ); document.write( "standing still and the other passing it
\n" ); document.write( "at 2 different speeds:
\n" ); document.write( " $\"+s%5B1%5D+%2B+s%5B2%5D+\"$ ( opposite direction speed )
\n" ); document.write( " $\"+s%5B2%5D+-+s%5B1%5D+\"$ ( same direction speed )
\n" ); document.write( "I picked $\"+s%5B2%5D+\"$ to be faster speed
\n" ); document.write( "--------------
\n" ); document.write( "The head of the moving train goes from the tail of the
\n" ); document.write( "still train to it's head ( 400 ft )
\n" ); document.write( "Then the tail of the moving train has to go from the
\n" ); document.write( "tail of the still train to it's head ( another 400 ft )
\n" ); document.write( "The moving train travels $\"+800+\"$ ft passing
\n" ); document.write( "the still train
\n" ); document.write( "---------------
\n" ); document.write( "(1) $\"+800+=+%28+s%5B1%5D+%2B+s%5B2%5D+%29%2A5+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+800+=+%28+s%5B2%5D+-+s%5B1%5D+%29%2A20+\"$
\n" ); document.write( "Speeds will be in ft/sec
\n" ); document.write( "----------------
\n" ); document.write( "(1) $\"+5s%281%29+%2B+5s%282%29+=+800+\"$
\n" ); document.write( "(2) $\"+-20s%5B1%5D+%2B+20s%282%29+=+800+\"$
\n" ); document.write( "----------------
\n" ); document.write( "Multiply both sides of (1) by $\"+4+\"$ and
\n" ); document.write( "add the equations
\n" ); document.write( "(1) $\"+20s%281%29+%2B+20s%282%29+=+3200+\"$
\n" ); document.write( "(2) $\"+-20s%5B1%5D+%2B+20s%282%29+=+800+\"$
\n" ); document.write( " $\"+40s%5B2%5D+=+4000+\"$
\n" ); document.write( " $\"+s%5B2%5D+=+100+\"$
\n" ); document.write( "substitute this into (1)
\n" ); document.write( "(1) $\"+5s%281%29+%2B+5%2A100+=+800+\"$
\n" ); document.write( "(1) $\"+5s%5B1%5D+=+800+-+500+\"$
\n" ); document.write( "(1) $\"+5s%5B1%5D+=+300+\"$
\n" ); document.write( "(1) $\"+s%5B1%5D+=+60+\"$
\n" ); document.write( "The faster train travels at 100 ft/sec
\n" ); document.write( "The slower train travels at 60 ft/sec
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"+800+=+%28+s%5B1%5D+%2B+s%5B2%5D+%29%2A5+\"$
\n" ); document.write( "(1) $\"+800+=+%28+60+%2B+100+%29%2A5+\"$
\n" ); document.write( "(1) $\"+800+=+160%2A5+\"$
\n" ); document.write( "(1) $\"+800+=+800+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+800+=+%28+s%5B2%5D+-+s%5B1%5D+%29%2A20+\"$
\n" ); document.write( "(2) $\"+800+=+%28+100+-+60+%29%2A20+\"$
\n" ); document.write( "(2) $\"+800+=+40%2A20+\"$
\n" ); document.write( "(2) $\"+800+=+800+\"$
\n" ); document.write( "OK \n" ); document.write( "

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