document.write( "Question 851788: A boat travels 15km/hr in still water. In travelling 45 km downstream from Town A to Town B, it completes the journey in 75 minutes less than it takes for the return journey. At what speed does the river flow?
\n" ); document.write( "Please explain simply. Apparently I am an idiot. \n" ); document.write( "

Algebra.Com's Answer #513002 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
It's not easy and probably not a
\n" ); document.write( "test of intelligence
\n" ); document.write( "Let $\"+c+\"$ = the speed of the river ( c for current )
\n" ); document.write( " $\"+15+%2B+c+\"$ = the speed of the boat going downstream
\n" ); document.write( " $\"+15+-+c+\"$ = the speed of the boat going upstream
\n" ); document.write( "Let $\"+t+\"$ = the time in hours to travel
\n" ); document.write( "from A to B going downstream
\n" ); document.write( " $\"+t+%2B+75%2F60+\"$ = the time in hours to travel
\n" ); document.write( "from B to A going upstream
\n" ); document.write( "-----------------------------------------
\n" ); document.write( "Equation for going downstream:
\n" ); document.write( "(1) $\"++45+=+%28+15+%2B+c+%29%2At+\"$
\n" ); document.write( "Equation for going upstream:
\n" ); document.write( "(2) $\"+45+=+%28+15+-+c+%29%2A%28+t+%2B+75%2F60+%29+\"$
\n" ); document.write( "---------------------------------
\n" ); document.write( "(2) $\"+45+=+%28+15+-+c+%29%2A%28+t+%2B+5%2F4+%29+\"$
\n" ); document.write( "(2) $\"+45+=+15t+-+c%2At+%2B+75%2F4+-+%285%2F4%29%2Ac+\"$
\n" ); document.write( "(2) $\"+45+=+t%2A%28+15+-+c+%29+%2B+75%2F4+-+%285%2F4%29%2Ac+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+t+=+45+%2F+%28+15+%2B+c+%29+\"$
\n" ); document.write( "substitute this into (2)
\n" ); document.write( "(2) $\"+45+=+%28+45+%2F+%28+15+%2B+c+%29+%29%2A%28+15+-+c+%29+%2B+75%2F4+-+%285%2F4%29%2Ac+\"$
\n" ); document.write( "Multiply both sides by $\"+4%2A%28+15+%2B+c+%29+\"$
\n" ); document.write( "(2)

\n" ); document.write( "(2) $\"+2700+%2B+180c+=+2700+-+180c+%2B+1125+%2B+75c+-+75c+-+5c%5E2+\"$
\n" ); document.write( "(2) $\"+360c+=+1125+-+5c%5E2+\"$
\n" ); document.write( "(2) $\"+5c%5E2+%2B+360c+-1125+=+0+\"$
\n" ); document.write( "(2) $\"+c%5E2+%2B+72c+-+225+=+0+\"$
\n" ); document.write( "Use quadratic formula
\n" ); document.write( " $\"+C+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"$ ( C and c are different )
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( " $\"+b+=+72+\"$
\n" ); document.write( " $\"+c+=+-225+\"$
\n" ); document.write( " $\"+C+=+%28+-72+%2B-+sqrt%28+72%5E2+-+4%2A1%2A%28-225%29+%29%29+%2F+%282%2A1%29+\"$
\n" ); document.write( " $\"+C+=+%28+-72+%2B-+sqrt%28+5184+%2B+900%29%29+%2F+2+\"$
\n" ); document.write( " $\"+C+=+%28+-72+%2B-+sqrt%28+6084%29%29+%2F+2+\"$
\n" ); document.write( " $\"+C+=+%28+-72+%2B-+78%29+%2F+2+\"$
\n" ); document.write( " $\"+C+=+6%2F2+\"$
\n" ); document.write( " $\"+C+=+3+\"$ ( can't use the negative square root )
\n" ); document.write( "The river flows at 3 km/hr
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"++45+=+%28+15+%2B+3+%29%2At+\"$
\n" ); document.write( "(1) $\"+45+=+18t+\"$
\n" ); document.write( "(1) $\"+t+=+2.5+\"$ hrs
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+45+=+%28+15+-+3+%29%2A%28+t+%2B+75%2F60+%29+\"$
\n" ); document.write( "(2) $\"+45+=+12t+%2B+15+\"$
\n" ); document.write( "(2) $\"+12t+=+30+\"$
\n" ); document.write( "(2) $\"+t+=+2.5+\"$ hrs
\n" ); document.write( "OK
\n" ); document.write( "There may be an easier way to solve this-
\n" ); document.write( "I just don't know what it is\r
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