document.write( "Question 179569: Tom's home is 1,800 m from his school. One morning he walked part of the way to school and then ran the rest. If it took him 20 minutes or less to get to school, and he walks at 70m/min and runs 210m/min, how far did he run? \n" ); document.write( "

Algebra.Com's Answer #134556 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I will write 2 equations:
\n" ); document.write( "1 for running
\n" ); document.write( "1 for walking
\n" ); document.write( "(1) $\"d%5Bw%5D+=+r%5Bw%5D%2At%5Bw%5D\"$
\n" ); document.write( "(2) $\"d%5Br%5D+=+r%5Br%5D%2At%5Br%5D\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"r%5Bw%5D+=+70\"$ m/min
\n" ); document.write( " $\"r%5Br%5D+=+210\"$ m/min
\n" ); document.write( " $\"d%5Bw%5D+%2B+d%5Br%5D+=+1800\"$ m
\n" ); document.write( " $\"t%5Bw%5D+%2B+t%5Br%5D+%3C=+20\"$ min
\n" ); document.write( "--------------------------
\n" ); document.write( "I can rewrite (1) and (2):
\n" ); document.write( "(1) $\"d%5Bw%5D+=+70t%5Bw%5D\"$ m
\n" ); document.write( "(2) $\"d%5Br%5D+=+210t%5Br%5D\"$ m
\n" ); document.write( "Now, from
\n" ); document.write( " $\"d%5Bw%5D+%2B+d%5Br%5D+=+1800\"$ I get
\n" ); document.write( " $\"d%5Br%5D+=+1800+-+d%5Bw%5D\"$
\n" ); document.write( "I'll substitute this in (2)
\n" ); document.write( "(2) $\"1800+-+d%5Bw%5D+=+210t%5Br%5D\"$ m
\n" ); document.write( "{2) $\"d%5Bw%5D+=+1800+-+210t%5Br%5D\"$ m
\n" ); document.write( "I'll subtract (1) from (2):
\n" ); document.write( "{2) $\"d%5Bw%5D+=+1800+-+210t%5Br%5D\"$
\n" ); document.write( "(1) $\"-d%5Bw%5D+=+-70t%5Bw%5D\"$
\n" ); document.write( " $\"0+=+1800+-+210t%5Br%5D+-+70t%5Bw%5D\"$
\n" ); document.write( " $\"70t%5Bw%5D+%2B+210t%5Br%5D+=+1800\"$
\n" ); document.write( "Divide both sides by $\"10\"$
\n" ); document.write( "(3) $\"7t%5Bw%5D+%2B+21t%5Br%5D+=+180\"$
\n" ); document.write( "from
\n" ); document.write( " $\"t%5Bw%5D+%2B+t%5Br%5D+%3C=+20\"$ min
\n" ); document.write( "If $\"t%5Bw%5D+%2B+t%5Br%5D+=+20\"$ min
\n" ); document.write( "Multiply each side by $\"7\"$
\n" ); document.write( "(4) $\"7t%5Bw%5D+%2B+7t%5Br%5D+=+140\"$ min
\n" ); document.write( "Subtract (4) from (3)
\n" ); document.write( "(3) $\"7t%5Bw%5D+%2B+21t%5Br%5D+=+180\"$
\n" ); document.write( "(4) $\"-7t%5Bw%5D+-+7t%5Br%5D+=+-140\"$
\n" ); document.write( " $\"14t%5Br%5D+=+40\"$
\n" ); document.write( " $\"t%5Br%5D+=+20%2F7\"$ min
\n" ); document.write( "and,since
\n" ); document.write( " $\"t%5Bw%5D+%2B+t%5Br%5D+=+20\"$ min
\n" ); document.write( " $\"t%5Bw%5D+=+20+-+t%5Br%5D\"$
\n" ); document.write( " $\"t%5Bw%5D+=+20+-+20%2F7\"$
\n" ); document.write( " $\"t%5Bw%5D+=+%28140+-+20%29%2F7\"$
\n" ); document.write( " $\"t%5Bw%5D+=+120%2F7\"$ min
\n" ); document.write( "The problem wants to know how far he ran
\n" ); document.write( "(2) $\"d%5Br%5D+=+210t%5Br%5D\"$ m
\n" ); document.write( " $\"d%5Br%5D+=+210%2A%2820%2F7%29\"$ m
\n" ); document.write( " $\"d%5Br%5D+=+600\"$ m
\n" ); document.write( "He ran 600 m
\n" ); document.write( "check answer:
\n" ); document.write( "I can rewrite (1) and (2):
\n" ); document.write( "(1) $\"d%5Bw%5D+=+70t%5Bw%5D\"$ m
\n" ); document.write( " $\"d%5Bw%5D+=+70%2A%28120%2F7%29\"$ m
\n" ); document.write( " $\"d%5Bw%5D+=+1200\"$ m
\n" ); document.write( "And, since
\n" ); document.write( " $\"d%5Bw%5D+%2B+d%5Br%5D+=+1800\"$ m
\n" ); document.write( " $\"600+%2B+1200+=+1800\"$
\n" ); document.write( " $\"1800+=+1800\"$
\n" ); document.write( "OK
\n" ); document.write( "I also looked at
\n" ); document.write( " $\"t%5Bw%5D+%2B+t%5Br%5D+%3C=+20\"$ min
\n" ); document.write( "If he spent a little more time running than
\n" ); document.write( "walking, say
\n" ); document.write( " $\"t%5Br%5D+=+21%2F7\"$
\n" ); document.write( "and
\n" ); document.write( " $\"t%5Bw%5D+=+119%2F7\"$
\n" ); document.write( " $\"d%5Bw%5D+%2B+d%5Br%5D+=+1820\"$ m
\n" ); document.write( "If he spent a little more time walking than running
\n" ); document.write( " $\"t%5Br%5D+=+19%2F7\"$
\n" ); document.write( " $\"t%5Bw%5D+=+121%2F7\"$
\n" ); document.write( " $\"d%5Bw%5D+%2B+d%5Br%5D+=+1780\"$ m
\n" ); document.write( "So, he has to spend at least as much time running
\n" ); document.write( "as he did \n" ); document.write( "

\n" );