document.write( "Question 402406: a boat travels 60 km upsteam in 5 hours. the boat travels the same direction downstream in 3 hours. what is the rate of the boat in still water? what is the rate of the current? \n" ); document.write( "

Algebra.Com's Answer #284686 by josmiceli(19441) $\"\"$ $\"About$

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\n" ); document.write( " $\"b+%2B+c\"$ = rate going downstream
\n" ); document.write( " $\"b+-+c\"$ = rate going upstream
\n" ); document.write( "------------
\n" ); document.write( "given:
\n" ); document.write( "upstream:
\n" ); document.write( "(1) $\"60+=+%28b+-+c%29%2A5\"$ km
\n" ); document.write( "downstream:
\n" ); document.write( "(2) $\"60+=+%28b+%2B+c%29%2A3\"$ km
\n" ); document.write( "------------
\n" ); document.write( "This is 2 equations and 2 unknowns
\n" ); document.write( "so it's solvable
\n" ); document.write( "(1) $\"5b+-+5c+=+60\"$
\n" ); document.write( "(2) $\"3b+%2B+3c+=+60\"$
\n" ); document.write( "Multiply both sides of (1) by $\"3\"$
\n" ); document.write( "and both sides of (2) by $\"5\"$
\n" ); document.write( "Then add the equations
\n" ); document.write( "(1) $\"15b+-+15c+=+180\"$
\n" ); document.write( "(2) $\"15b+%2B+15c+=+300\"$
\n" ); document.write( " $\"30b+=+480\"$
\n" ); document.write( " $\"b+=+16\"$
\n" ); document.write( "Plug this back into (1)
\n" ); document.write( "(1) $\"5%2A16+-+5c+=+60\"$
\n" ); document.write( " $\"80+-+5c+=+60\"$
\n" ); document.write( " $\"5c+=+20\"$
\n" ); document.write( " $\"c+=+4\"$
\n" ); document.write( "16 km/hr is the rate of the boat in still water
\n" ); document.write( "4 km/hr is the rate of the current
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"60+=+%2816+-+4%29%2A5\"$ km
\n" ); document.write( " $\"60+=+12%2A5\"$
\n" ); document.write( " $\"60+=+60\"$
\n" ); document.write( "(2) $\"60+=+%2816+%2B+4%29%2A3\"$ km
\n" ); document.write( " $\"60+=+20%2A3\"$
\n" ); document.write( " $\"60+=+60\"$
\n" ); document.write( "OK \n" ); document.write( "

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