document.write( "Question 876747: Write an equation that can be used to solve the problem. Emily's school bus averages 28 mi/h, including stops. One day Emily forgot her backpack. Her mom left home 15 minutes (0.25h) after Emily and travled at an average speed of 42 mi/h. How long will it take Emily's mom to catch the bus? \n" ); document.write( "

Algebra.Com's Answer #529003 by josmiceli(19441) $\"\"$ $\"About$

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How much of a head start does the bus have?
\n" ); document.write( " $\"+d%5B1%5D+=+28%2A%28+.25+%29+\"$
\n" ); document.write( " $\"+d%5B1%5D+=+7+\"$ mi
\n" ); document.write( "------------------
\n" ); document.write( "Start a stopwatch when her mom leaves
\n" ); document.write( "Let $\"+t+\"$ = time on stopwatch when she
\n" ); document.write( "catches up with the bus
\n" ); document.write( "Let $\"+d+\"$ = the distance that her mom
\n" ); document.write( "travels until she catches bus
\n" ); document.write( "----------------------
\n" ); document.write( "The buses equation:
\n" ); document.write( "(1) $\"+d+-+7+=+28t+\"$
\n" ); document.write( "Mom's equation:
\n" ); document.write( "(2) $\"+d+=+42t+\"$
\n" ); document.write( "----------------
\n" ); document.write( "(1) $\"+d+=+28t+%2B+7+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+28t+%2B+7+=+42t+\"$
\n" ); document.write( " $\"+14t+=+7+\"$
\n" ); document.write( " $\"+t+=+1%2F2+\"$ hr
\n" ); document.write( "Emily's mom will catch the bus in 30 min
\n" ); document.write( "-------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+d+-+7+=+28%2A%28+1%2F2+%29+\"$
\n" ); document.write( "(1) $\"+d+=+21+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+d+=+42%2A%28+1%2F2+%29+\"$
\n" ); document.write( "(2) $\"+d+=+21+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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