document.write( "Question 389197: Steven left Town A and walked towards Town B at a speed of 100m/min. At the same time, Jason and Melvin started from Town B and walked towards Town A at a speed of 80m/min and 75m/min respectively. If Steven met Melvin six minutes after passing Jason, find the distance between Town A and Town B. \n" ); document.write( "

Algebra.Com's Answer #275737 by josmiceli(19441) $\"\"$ $\"About$

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Stephen meets Jason in $\"t\"$ min
\n" ); document.write( "Stephen went $\"d%5B1%5D\"$ m and
\n" ); document.write( "Jason went $\"d%5B2%5D\"$ m
\n" ); document.write( "I can write 2 equations:
\n" ); document.write( " $\"d%5B1%5D+=+100t\"$ m
\n" ); document.write( " $\"d%5B2%5D+=+80t\"$ m
\n" ); document.write( "Now add the equations:
\n" ); document.write( " $\"d%5B1%5D+%2B+d%5B2%5D+=+180t\"$ m
\n" ); document.write( "Let $\"d%5B1%5D+%2B+d%5B2%5D+=+d\"$ , the distance between the towns
\n" ); document.write( " $\"d+=+180t\"$
\n" ); document.write( "In 8 more min, stephen goes $\"d%5B3%5D+=+100%2A8\"$ m further
\n" ); document.write( " $\"d%5B3%5D+=+800\"$ m , so he went $\"d%5B1%5D+%2B+d%5B3%5D+=+100t+%2B+800\"$
\n" ); document.write( "total distance to meet Melvin
\n" ); document.write( "Now I want to know how far Melvin went in $\"t+%2B+8\"$ min
\n" ); document.write( "He went $\"d%5B4%5D+=+75%2A%28t+%2B+8%29\"$ m
\n" ); document.write( " $\"d%5B4%5D+=+75t+%2B+600\"$ m
\n" ); document.write( "Note that $\"d%5B1%5D+%2B+d%5B3%5D+%2B+d%5B4%5D+=+d\"$ the distance between the towns
\n" ); document.write( " $\"d+=+100t+%2B+800+%2B+75t+%2B+600\"$
\n" ); document.write( "and, from before, I said $\"d+=+180t\"$ , so
\n" ); document.write( " $\"180t+=+175t+%2B+1400\"$
\n" ); document.write( " $\"5t+=+1400\"$
\n" ); document.write( " $\"t+=+280\"$
\n" ); document.write( "and, if $\"d+=+180t\"$
\n" ); document.write( " $\"d+=+180%2A280\"$
\n" ); document.write( " $\"d+=+50400\"$ m
\n" ); document.write( "The distance between towns A and B is 50.4 km
\n" ); document.write( "check answer:
\n" ); document.write( " $\"d%5B1%5D+=+100t\"$
\n" ); document.write( " $\"d%5B1%5D+=+100%2A280\"$
\n" ); document.write( " $\"d%5B1%5D+=+28000\"$ m
\n" ); document.write( "and
\n" ); document.write( " $\"d%5B2%5D+=+80t\"$
\n" ); document.write( " $\"d%5B2%5D+=+80%2A280\"$
\n" ); document.write( " $\"d%5B2%5D+=+22400\"$
\n" ); document.write( " $\"d%5B1%5D+%2B+d%5B2%5D+=+28000+%2B+22400\"$ m
\n" ); document.write( " $\"d+=+50400\"$ m
\n" ); document.write( "OK
\n" ); document.write( " $\"d%5B3%5D+=+800\"$ m
\n" ); document.write( " $\"d%5B1%5D+%2B+d%5B3%5D+%2B+d%5B4%5D+=+28000+%2B+800+%2B+75t+%2B+600\"$
\n" ); document.write( " $\"d+=+28000+%2B+800+%2B+75%2A280+%2B+600\"$
\n" ); document.write( " $\"d+=+28800+%2B+21000+%2B+600\"$
\n" ); document.write( " $\"d+=+50400\"$
\n" ); document.write( "OK \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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