document.write( "Question 545887: a small motorboat travels 14mph in still water. It takes 6 hours longer to travel 59 miles going upstream than it does down stream. Find the rate of the current. \n" ); document.write( "

Algebra.Com's Answer #355777 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"w\"$ = rate of current
\n" ); document.write( "Let $\"b\"$ = rate of boat in still water
\n" ); document.write( " $\"+b+-+w+\"$ = rate going against current
\n" ); document.write( " $\"+b+%2B+w+\"$ = rate going with current
\n" ); document.write( "Let $\"t\"$ = time for boat to go $\"59\"$ mi with current
\n" ); document.write( "-------------
\n" ); document.write( "given:
\n" ); document.write( "equation for going downstream ( with current )
\n" ); document.write( " $\"+59+=+%28+b+%2B+w+%29%2A+t+\"$
\n" ); document.write( " $\"+59+=+%28+14+%2B+w+%29%2At+\"$
\n" ); document.write( "(1) $\"+t+=+59+%2F+%28+14+%2B+w+%29+\"$
\n" ); document.write( "equation for going upstream ( against current )
\n" ); document.write( " $\"+59+=+%28+b+-+w+%29%2A%28+t+%2B+6+%29+\"$
\n" ); document.write( " $\"+59+=+%28+14+-+w+%29%2A%28t+%2B+6+%29+\"$
\n" ); document.write( " $\"+59+=+14t+-+w%2At+%2B+84+-+6w+\"$
\n" ); document.write( "(2) $\"+t%2A%28+w+-+14+%29+%2B+6w+=+84+-+59+\"$
\n" ); document.write( "(2) $\"+t%2A%28+w+-+14+%29+%2B+6w+=+25+\"$
\n" ); document.write( "------------------
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+%28+59%2F%28+14+%2B+w+%29%29%2A%28+w+-+14+%29+%2B+6w+=+25+\"$
\n" ); document.write( "multiply both sides by $\"+14+%2B+w+%29+\"$
\n" ); document.write( "(2) $\"+59%2A%28+w+-+14+%29+%2B+6c%2A%28+14+%2B+w+%29+=+25%2A%28+14+%2B+w+%29+\"$
\n" ); document.write( "(2) $\"+59w+-+826+%2B+84w+%2B+6w%5E2+=+350+%2B+25w+\"$
\n" ); document.write( "(2) $\"+6w%5E2+%2B+84w+%2B+59w+-+25w+-+825+-+350+=+0+\"$
\n" ); document.write( "(2) $\"+6w%5E2+%2B+118w+-+1175+=+0+\"$
\n" ); document.write( "Use quadratic equation
\n" ); document.write( " $\"w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+6+\"$
\n" ); document.write( " $\"+b+=+118+\"$
\n" ); document.write( " $\"+c+=+-1175+\"$
\n" ); document.write( " $\"w+=+%28-118++%2B-+sqrt%28+118%5E2-4%2A6%2A%28-1175%29+%29%29%2F%282%2A6%29+\"$
\n" ); document.write( " $\"w+=+%28-118++%2B-+sqrt%28+13924+%2B+28200+%29%29+%2F+12+\"$
\n" ); document.write( " $\"w+=+%28-118++%2B-+sqrt%28+42124+%29%29+%2F+12+\"$
\n" ); document.write( " $\"+w+=+%28+-118+%2B+205.24%29+%2F+12+\"$
\n" ); document.write( " $\"+w+=+87.24%2F12+\"$
\n" ); document.write( " $\"+w+=+7.27+\"$
\n" ); document.write( "The rate of the current is 7.27 mi/hr
\n" ); document.write( "check answer:
\n" ); document.write( " $\"+59+=+%28+14+%2B+w+%29%2At+\"$
\n" ); document.write( " $\"+59+=+%28+14+%2B+7.27+%29%2At+\"$
\n" ); document.write( " $\"+59+=+21.27t+\"$
\n" ); document.write( " $\"+t+=+2.774+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+59+=+%28+14+-+w+%29%2A%28t+%2B+6+%29+\"$
\n" ); document.write( " $\"+59+=+%28+14+-+7.27+%29%2A%28t+%2B+6+%29+\"$
\n" ); document.write( " $\"+59+=+6.73%2A%28+t+%2B+6+%29+\"$
\n" ); document.write( " $\"+59+=+6.73t+%2B+40.38+\"$
\n" ); document.write( " $\"+6.73t+=+59+-+40.38+\"$
\n" ); document.write( " $\"+6.73t+=+18.62+\"$
\n" ); document.write( " $\"+t+=+2.767+\"$
\n" ); document.write( "This looks close enough \n" ); document.write( "

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