document.write( "Question 273172: Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #199592 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Write 2 equations:
\n" ); document.write( "Going to work:
\n" ); document.write( "\"d+=+r%5B1%5D%2At%5B1%5D\"
\n" ); document.write( "Coming home from work:
\n" ); document.write( "\"d+=+r%5B2%5D%2At%5B2%5D\"
\n" ); document.write( "---------------------
\n" ); document.write( "given:
\n" ); document.write( "\"r%5B1%5D+=+45\" mi/hr
\n" ); document.write( "\"r%5B2%5D+=+30\" mi/hr
\n" ); document.write( "\"t%5B1%5D+%2B+t%5B2%5D+=+1\" hr
\n" ); document.write( "---------------------
\n" ); document.write( "\"d+=+45t%5B1%5D\"
\n" ); document.write( "\"d+=+30t%5B2%5D\"
\n" ); document.write( "then
\n" ); document.write( "\"d%2F45+=+t%5B1%5D\"
\n" ); document.write( "\"d%2F30+=+t%5B2%5D\"
\n" ); document.write( "Add the equations
\n" ); document.write( "\"d%2A%281%2F45+%2B+1%2F30%29+=+t%5B1%5D+%2B+t%5B2%5D\"
\n" ); document.write( "\"d+=+1%2F%281%2F45+%2B+1%2F30%29\"
\n" ); document.write( "\"d+=+1%2F%282%2F90+%2B+3%2F90%29\"
\n" ); document.write( "\"d+=+1%2F%285%2F90%29\"
\n" ); document.write( "\"d+=+18\" mi
\n" ); document.write( "Esther drove 18 mi to work
\n" ); document.write( "check:
\n" ); document.write( "\"d%2F45+=+t%5B1%5D\"
\n" ); document.write( "\"t%5B1%5D+=+18%2F45\"
\n" ); document.write( "and
\n" ); document.write( "\"d%2F30+=+t%5B2%5D\"
\n" ); document.write( "\"t%5B2%5D+=+18%2F30\"
\n" ); document.write( "\"t%5B1%5D+%2B+t%5B2%5D+=+18%2F45+%2B+18%2F30\"
\n" ); document.write( "\"t%5B1%5D+%2B+t%5B2%5D+=+18%2A%281%2F45+%2B+1%2F30%29\"
\n" ); document.write( "\"t%5B1%5D+%2B+t%5B2%5D+=+18%2A%282%2F90+%2B+3%2F90%29\"
\n" ); document.write( "\"t%5B1%5D+%2B+t%5B2%5D+=+18%2A%285%2F90%29\"
\n" ); document.write( "\"t%5B1%5D+%2B+t%5B2%5D+=+18%2A%281%2F18%29\"
\n" ); document.write( "\"t%5B1%5D+%2B+t%5B2%5D+=+1\" hr
\n" ); document.write( "OK\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );