document.write( "Question 182513: 1.
\n" ); document.write( "Solve\r
\n" ); document.write( "\n" ); document.write( "(3a-5)(a²+4a+3) + (2a+2)(a+3) = (a-3)(a+1)\r
\n" ); document.write( "\n" ); document.write( "2.
\n" ); document.write( "Rachel allows herself 1 hour to reach a sale appointment 50 mile s away. After she has driven 30 miles, she realizes that she must increase her speed by 15 miles per hour in order to get there on time. What was her speed for the first 30 miles? \n" ); document.write( "

Algebra.Com's Answer #137005 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
For 1st leg:
\n" ); document.write( "(a) $\"d%5B1%5D+=+r%5B1%5D%2At%5B1%5D\"$
\n" ); document.write( "For 2nd leg:
\n" ); document.write( "(b) $\"d%5B2%5D+=+r%5B2%5D%2At%5B2%5D\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"t%5B1%5D+%2B+t%5B2%5D+=+1\"$ hrs
\n" ); document.write( " $\"d%5B1%5D+=+30\"$ mi
\n" ); document.write( " $\"d%5B1%5D+%2B+d%5B2%5D+=+50\"$ mi
\n" ); document.write( " $\"r%5B2%5D+=+r%5B1%5D+%2B+15\"$ mi/hr
\n" ); document.write( "----------------------------
\n" ); document.write( "Now rewrite (a) and (b)
\n" ); document.write( "(a) $\"d%5B1%5D+=+r%5B1%5D%2At%5B1%5D\"$
\n" ); document.write( "(a) $\"30+=+r%5B1%5D%2At%5B1%5D\"$
\n" ); document.write( "and
\n" ); document.write( "(b) $\"d%5B2%5D+=+r%5B2%5D%2At%5B2%5D\"$
\n" ); document.write( "(b) $\"50+-+d%5B1%5D+=+%28r%5B1%5D+%2B+15%29%2A%281+-+t%5B1%5D%29\"$
\n" ); document.write( "(b) $\"50+-+d%5B1%5D+=+r%5B1%5D+%2B+15+-+r%5B1%5D%2At%5B1%5D+-+15t%5B1%5D\"$
\n" ); document.write( "Note that $\"r%5B1%5D%2At%5B1%5D+=+d%5B1%5D\"$ and $\"d%5B1%5D+=+30\"$
\n" ); document.write( "(b) $\"20+=+r%5B1%5D+-+15t%5B1%5D+-+15+\"$
\n" ); document.write( "(b) $\"15t%5B1%5D+=+r%5B1%5D+-+35\"$
\n" ); document.write( "From (a)
\n" ); document.write( "(a) $\"r%5B1%5D+=+30%2Ft%5B1%5D\"$
\n" ); document.write( "(c) $\"15t%5B1%5D+=+30%2Ft%5B1%5D+-+35\"$
\n" ); document.write( "Multiply both sides by $\"t%5B1%5D\"$
\n" ); document.write( "(c) $\"15%28t%5B1%5D%29%5E2+=+30+-+35t%5B1%5D\"$
\n" ); document.write( "(c) $\"3%28t%5B1%5D%29%5E2+%2B+7t%5B1%5D+-+6+=+0\"$
\n" ); document.write( "I'll say $\"t%5B1%5D+=+x\"$ for now and use quadratic formula
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"a+=+3\"$
\n" ); document.write( " $\"b+=+7\"$
\n" ); document.write( " $\"c+=+-6\"$
\n" ); document.write( " $\"x+=+%28-7+%2B-+sqrt%28+7%5E2-4%2A3%2A%28-6%29+%29%29%2F%282%2A3%29+\"$
\n" ); document.write( " $\"x+=+%28-7+%2B-+sqrt%28+49+%2B+72+%29%29%2F6+\"$
\n" ); document.write( " $\"x+=+%28-7+%2B-+sqrt%28+121+%29%29%2F6+\"$
\n" ); document.write( " $\"x+=+%28-7+%2B-+11%29%2F6+\"$
\n" ); document.write( " $\"x+=+-3\"$ (I can't use a negative answer)
\n" ); document.write( " $\"x+=+2%2F3\"$
\n" ); document.write( "and, since $\"x+=+t%5B1%5D\"$ ,
\n" ); document.write( " $\"t%5B1%5D+=+2%2F3\"$
\n" ); document.write( "(a) $\"30+=+r%5B1%5D%2At%5B1%5D\"$
\n" ); document.write( " $\"30+=+r%5B1%5D%2A%282%2F3%29\"$
\n" ); document.write( " $\"r%5B1%5D+=+%283%2F2%29%2A30\"$
\n" ); document.write( " $\"r%5B1%5D+=+45\"$ mi/hr answer
\n" ); document.write( "check answer:
\n" ); document.write( "(a) $\"30+=+r%5B1%5D%2At%5B1%5D\"$
\n" ); document.write( "(b) $\"50+-+d%5B1%5D+=+%28r%5B1%5D+%2B+15%29%2A%281+-+t%5B1%5D%29\"$
\n" ); document.write( "----------------------
\n" ); document.write( "(a) $\"30+=+45%2A%282%2F3%29\"$
\n" ); document.write( "(a) $\"30+=+30\"$
\n" ); document.write( "(b) $\"50+-+30+=+%2845+%2B+15%29%2A%281+-+2%2F3%29\"$
\n" ); document.write( "(b) $\"20+=+%2845+%2B+15%29%2A%281+-+2%2F3%29\"$
\n" ); document.write( "(b) $\"20+=+60%2A%281%2F3%29\"$
\n" ); document.write( "(b) $\"20+=+20\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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