document.write( "Question 518231: the rate of the boat in still water is 8 mph. At this rate a 30 mile trip downstream takes the same amount of time as an 18 mile trip upstream. What is the rate of the current? \n" ); document.write( "

Algebra.Com's Answer #345102 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+s+\"$ = rate in still water
\n" ); document.write( "Let $\"+c+\"$ = rate of current
\n" ); document.write( "going downstream:
\n" ); document.write( "(1) $\"+d%5B1%5D+=+%28+s+%2B+c+%29%2At+\"$
\n" ); document.write( "Going upstream:
\n" ); document.write( "(2) $\"+d%5B2%5D+=+%28+s+-+c+%29%2At+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "given:
\n" ); document.write( " $\"+d%5B1%5D+=+30+\"$ mi
\n" ); document.write( " $\"+d%5B2%5D+=+18+\"$ mi
\n" ); document.write( " $\"+s+=+8+\"$ mi/hr
\n" ); document.write( "---------------
\n" ); document.write( "(1) $\"+30+=+%28+8+%2B+c+%29%2At+\"$
\n" ); document.write( "(2) $\"+18+=+%28+8+-+c+%29%2At+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "(1) $\"+30+=+8t+%2B+c%2At+\"$
\n" ); document.write( "(2) $\"+18+=+8t+-+c%2At+\"$
\n" ); document.write( "Add the equations
\n" ); document.write( " $\"+48+=+16t+\"$
\n" ); document.write( " $\"+t+=+3+\"$ hrs
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+30+=+8t+%2B+c%2At+\"$
\n" ); document.write( "(1) $\"+30+=+24+%2B+3c+\"$
\n" ); document.write( "(1) $\"+3c+=+6+\"$
\n" ); document.write( "(1) $\"+c+=+2+\"$
\n" ); document.write( "The rate of the current is 2 mi/hr
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+30+=+%28+8+%2B+c+%29%2At+\"$
\n" ); document.write( "(1) $\"+30+=+%28+8+%2B+2+%29%2A3+\"$
\n" ); document.write( "(1) $\"+30+=+10%2A3+\"$
\n" ); document.write( "OK \n" ); document.write( "

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