document.write( "Question 739431: A motorboat heads upstream a distance of 24 miles on a river with current running 3 miles per hour. The trip up and back takes 6 hours. Assuming the motorboat maintained a constant speed relative to the water, what was it's speed? \n" ); document.write( "

Algebra.Com's Answer #451117 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The speed of the boat going upstream is
\n" ); document.write( " $\"+s+-+3+\"$ mi/hr
\n" ); document.write( "The speed of the boat going downstream is
\n" ); document.write( " $\"+s+%2B+3+\"$ mi/hr
\n" ); document.write( "where $\"+s+\"$ = the boat's speed in still water
\n" ); document.write( "Let $\"+t+\"$ = the time in hrs for the boat to go upstream
\n" ); document.write( "-----------------
\n" ); document.write( "Going upstream:
\n" ); document.write( "(1) $\"+24+=+%28+s+-+3+%29%2At+\"$
\n" ); document.write( "Going downstream:
\n" ); document.write( "(2) $\"+24+=+%28+s+%2B+3+%29%2A%28+6+-+t+%29+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "(2) $\"+24+=+6s+%2B+18+-+s%2At+-+3t+\"$
\n" ); document.write( "(2) $\"+6s+-+s%2At+-+3t+=+6+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+s%2At++=+3t+%2B+24+\"$
\n" ); document.write( " -------------------
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+6s+-+3t+-+24+-+3t+=+6+\"$
\n" ); document.write( "(2) $\"+6t+=+6s+-+30+\"$
\n" ); document.write( "(2) $\"+t+=+s+-+5+\"$
\n" ); document.write( "Substitute this back into (1)
\n" ); document.write( "(1) $\"+24+=+%28+s+-+3+%29%2A%28+s-5+%29+\"$
\n" ); document.write( "(1) $\"+24+=+s%5E2+-+8s+%2B+15+\"$
\n" ); document.write( "(1) $\"+s%5E2+-+8s+-+9+=+0+\"$
\n" ); document.write( "(1) $\"+%28+s+-+9+%29%2A%28+s+%2B+1+%29+=+0+\"$ ( by inspection )
\n" ); document.write( " $\"+s+=+9+\"$ ( can't use $\"+s+=+-1+\"$ )
\n" ); document.write( "The boats speed is 9 mi/hr without a current
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+24+=+%28+9+-+3+%29%2At+\"$
\n" ); document.write( "(1) $\"+24+=+6t+\"$
\n" ); document.write( "(1) $\"+t+=+4+\"$ hrs
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+24+=+%28+9+%2B+3+%29%2A%28+6+-+t+%29+\"$
\n" ); document.write( "(2) $\"+24+=+12%2A%28+6+-+t+%29+\"$
\n" ); document.write( "(2) $\"+24+=+72+-+12t+\"$
\n" ); document.write( "(2) $\"+12t+=+72+-+24+\"$
\n" ); document.write( "(2) $\"+12t+=+48+\"$
\n" ); document.write( "(2) $\"+t+=+4+\"$ hrs
\n" ); document.write( "OK\r
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