document.write( "Question 286193: A Car is driven 280 mi. if it had gone 5mph faster, it could have made the trip in 1hr less time. What is the speed? \n" ); document.write( "

Algebra.Com's Answer #207546 by josmiceli(19441) $\"\"$ $\"About$

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Write 2 equations, 1 for each case:
\n" ); document.write( " $\"d+=+r%2At\"$
\n" ); document.write( "case #1
\n" ); document.write( " $\"280+=+rt\"$
\n" ); document.write( " $\"280+=+%28r+%2B+5%29%2A%28t+-+1%29\"$
\n" ); document.write( " $\"280+=+rt+%2B+5t+-+r+-+5\"$
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"280+=+280+%2B+5t+-+r+-+5\"$
\n" ); document.write( " $\"0+=+5t+-+r+-+5\"$
\n" ); document.write( " $\"r+=+5t+-+5\"$
\n" ); document.write( "Substituting again:
\n" ); document.write( " $\"280+=+%285t+-+5%29%2At\"$
\n" ); document.write( " $\"280+=+5t%5E2+-+5t\"$
\n" ); document.write( " $\"t%5E2+-+t+-+56+=+0\"$
\n" ); document.write( " $\"%28t+%2B+7%29%28t+-+8%29+=+0\"$
\n" ); document.write( " $\"t\"$ can't be negative, so $\"t+=+8\"$
\n" ); document.write( "and
\n" ); document.write( " $\"280+=+rt\"$
\n" ); document.write( " $\"280+=+r%2A8\"$
\n" ); document.write( " $\"r+=+35\"$ mi/hr
\n" ); document.write( "check answer:
\n" ); document.write( " $\"280+=+%28r+%2B+5%29%2A%28t+-+1%29\"$
\n" ); document.write( " $\"280+=+%2835+%2B+5%29%2A%28t+-+1%29\"$
\n" ); document.write( " $\"280+=+40t+-+40\"$
\n" ); document.write( " $\"320+=+40t\"$
\n" ); document.write( " $\"t+=+8\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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