document.write( "Question 874839: A motorboat travels 300 mi in 6 hours going upstream. It travels 456 mi going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current? \n" ); document.write( "

Algebra.Com's Answer #527814 by mananth(16946) $\"\"$ $\"About$

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300 / ( x - y )= 6
\n" ); document.write( "6 ( x - y ) = 4
\n" ); document.write( "6 x - 6 y = 300 ....................1
\n" ); document.write( "
\n" ); document.write( "456 / ( x + y )= 4
\n" ); document.write( "4 ( x + y ) = 456
\n" ); document.write( "4 x + 4 y = 456 ...............2
\n" ); document.write( "Multiply (1) by 2
\n" ); document.write( "Multiply (2) by 3
\n" ); document.write( "we get
\n" ); document.write( "12 x + -12 y = 600
\n" ); document.write( "12 x + 12 y = 1,368
\n" ); document.write( "24 x = 1,968
\n" ); document.write( "/ 24
\n" ); document.write( "x = 82 mph
\n" ); document.write( "
\n" ); document.write( "plug value of x in (1) y
\n" ); document.write( "6 x -6 y = 300
\n" ); document.write( "492 -6 -492 = 300
\n" ); document.write( "-6 y = 300
\n" ); document.write( "-6 y = -192 mph
\n" ); document.write( " y = 32
\n" ); document.write( "boat speed 82 mph
\n" ); document.write( "current speed 32 mph
\n" ); document.write( " \n" ); document.write( "

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