document.write( "Question 214879: A tug tows a bard 24 miles up a river at 10mph and returns down the river at 12 mph. The entire trip takes 5.5 hours. What is the rate of the river's current?\r
\n" ); document.write( "\n" ); document.write( "Since this problem doesn't provide the elapsed time of each trip, I am having trouble setting it up. \n" ); document.write( "

Algebra.Com's Answer #162347 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll write 2 equations, 1 for upriver
\n" ); document.write( "and 1 for downriver.
\n" ); document.write( " $\"d%5Bu%5D+=+r%5Bu%5D%2At%5Bu%5D\"$
\n" ); document.write( "and
\n" ); document.write( " $\"d%5Bd%5D+=+r%5Bd%5D%2At%5Bd%5D\"$
\n" ); document.write( "Let the rate of the river's current = $\"r%5Bc%5D\"$
\n" ); document.write( "Let $\"r%5Bb%5D\"$ = the rate of the boat in still water
\n" ); document.write( "given:
\n" ); document.write( " $\"d%5Bu%5D+=+24\"$ mi
\n" ); document.write( " $\"d%5Bd%5D+=+24\"$ mi
\n" ); document.write( " $\"r%5Bu%5D+=+10\"$ mi/hr
\n" ); document.write( " $\"r%5Bd%5D+=+12\"$ mi/hr
\n" ); document.write( " $\"t%5Bu%5D+%2B+t%5Bd%5D+=+5.5\"$ hr
\n" ); document.write( "--------------------------
\n" ); document.write( " $\"d%5Bu%5D+=+r%5Bu%5D%2At%5Bu%5D\"$
\n" ); document.write( " $\"24+=+10%2At%5Bu%5D\"$
\n" ); document.write( "and
\n" ); document.write( " $\"24+=+12%2At%5Bd%5D\"$
\n" ); document.write( "From these,
\n" ); document.write( " $\"t%5Bu%5D+=+2.4\"$
\n" ); document.write( " $\"t%5Bd%5D+=+2\"$
\n" ); document.write( "Let $\"r%5Bu%5D+=+r%5Bb%5D+-+r%5Bc%5D\"$
\n" ); document.write( "Let $\"r%5Bd%5D+=+r%5Bb%5D+%2B+r%5Bc%5D\"$
\n" ); document.write( "and
\n" ); document.write( " $\"r%5Bb%5D+=+r%5Bu%5D+%2B+r%5Bc%5D\"$
\n" ); document.write( " $\"r%5Bb%5D+=+r%5Bd%5D+-+r%5Bc%5D\"$
\n" ); document.write( " $\"r%5Bb%5D+=+10+%2B+r%5Bc%5D\"$
\n" ); document.write( " $\"r%5Bb%5D+=+12+-+r%5Bc%5D\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"10+%2B+r%5Bc%5D+=+12+-+r%5Bc%5D\"$
\n" ); document.write( " $\"2r%5Bc%5D+=+2\"$
\n" ); document.write( " $\"r%5Bc%5D+=+1\"$ mi/hr
\n" ); document.write( "The rate of the current is 1 mi/hr
\n" ); document.write( "check answer:
\n" ); document.write( " $\"d%5Bu%5D+=+r%5Bu%5D%2At%5Bu%5D\"$
\n" ); document.write( " $\"d%5Bu%5D+=+%28r%5Bb%5D+-+r%5Bc%5D%29%2At%5Bu%5D\"$
\n" ); document.write( " $\"24+=+%28r%5Bb%5D+-+1%29%2A2.4\"$
\n" ); document.write( " $\"24+=+2.4r%5Bb%5D+-+2.4\"$
\n" ); document.write( " $\"2.4r%5Bb%5D+=+26.4\"$
\n" ); document.write( " $\"r%5Bb%5D+=+11\"$ mi/hr
\n" ); document.write( "and
\n" ); document.write( " $\"d%5Bd%5D+=+r%5Bd%5D%2At%5Bd%5D\"$
\n" ); document.write( " $\"d%5Bd%5D+=+%28r%5Bb%5D+%2B+r%5Bc%5D%29%2At%5Bd%5D\"$
\n" ); document.write( " $\"24+=+%28r%5Bb%5D+%2B+1%29%2A2\"$
\n" ); document.write( " $\"24+=+2r%5Bb%5D+%2B+2\"$
\n" ); document.write( " $\"2r%5Bb%5D+=+22\"$
\n" ); document.write( " $\"r%5Bb%5D+=+11\"$ mi/hr
\n" ); document.write( "OK\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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