document.write( "Question 698181: If you travel 180 miles and then travel 15 Mph faster and get there an hour sooner how fast we're u going \n" ); document.write( "

Algebra.Com's Answer #430504 by josmiceli(19441) $\"\"$ $\"About$

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$\"+d+=+r%2At+\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"+d+=+180+\"$ mi
\n" ); document.write( "Let $\"+r+\"$ = usual rate
\n" ); document.write( "Let $\"+t+\"$ = time to go 180 mi at usual rate
\n" ); document.write( " $\"+r+%2B+15+\"$ = faster rate
\n" ); document.write( " $\"+t+-+1+\"$ = time to go 180 mi at faster rate
\n" ); document.write( "--------------
\n" ); document.write( "At usual rate:
\n" ); document.write( "(1) $\"+180+=+r%2At+\"$
\n" ); document.write( "At faster rate:
\n" ); document.write( "(2) $\"+180+=+%28+r+%2B+15+%29%2A%28+t+-+1+%29+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(2) $\"+180+=+r%2At+%2B+15t+-+r+-+15+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+t+=+180%2Fr+\"$
\n" ); document.write( "Substitute this into (2)
\n" ); document.write( "(2) $\"+180+=+r%2A%28180%2Fr%29+%2B+15%2A%28180%2Fr%29+-+r+-+15+\"$
\n" ); document.write( "(2) $\"+15%2A%28180%2Fr%29+-+r+=+15+\"$
\n" ); document.write( "Multiply both sides by $\"+r+\"$
\n" ); document.write( "(2) $\"+2700++-+r%5E2+=+15r+\"$
\n" ); document.write( "(2) $\"+r%5E2+%2B+15r+-+2700+=+0+\"$
\n" ); document.write( "Use quadratic formula
\n" ); document.write( " $\"+r+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( " $\"+b+=+15+\"$
\n" ); document.write( " $\"+c+=+-2700+\"$
\n" ); document.write( " $\"+r+=+%28+-15+%2B-+sqrt%28+15%5E2+-+4%2A1%2A%28-2700%29+%29%29+%2F+%282%2A1%29+\"$
\n" ); document.write( " $\"+r+=+%28+-15+%2B-+sqrt%28+225+%2B+10800+%29%29+%2F+2+\"$
\n" ); document.write( " $\"+r+=+%28+-15+%2B-+sqrt%28+11025+%29%29+%2F+2+\"$
\n" ); document.write( " $\"+r+=+%28+-15+%2B+105%29+%2F+2+\"$
\n" ); document.write( " $\"+r+=+90%2F2+\"$
\n" ); document.write( " $\"+r+=+45+\"$
\n" ); document.write( " $\"+r+%2B+15+=+60+\"$
\n" ); document.write( "Your usual speed is 45 mi/hr
\n" ); document.write( "Your faster speed is 60 mi/hr
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"+t+=+180%2Fr+\"$
\n" ); document.write( "(1) $\"+t+=+180%2F45+\"$
\n" ); document.write( "(1) $\"+t+=+4+\"$ hrs
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+180+=+%28+45+%2B+15+%29%2A%28+4+-+1+%29+\"$
\n" ); document.write( "(2) $\"+180+=+60%2A3+\"$
\n" ); document.write( "(20 $\"+180+=+180+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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