document.write( "Question 947130: M can do a piece of work in 4 hours, N and P together in 3 hours, and M and P together in 2 hours. How long will N alone take to do it? \n" ); document.write( "

Algebra.Com's Answer #577840 by Fombitz(32388) $\"\"$ $\"About$

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Rate x Time = Output
\n" ); document.write( "Let's choose the output to be 100%.
\n" ); document.write( " $\"R%5Bm%5D%2A4=100\"$
\n" ); document.write( "1. $\"R%5Bm%5D=25\"$
\n" ); document.write( ".
\n" ); document.write( ".\r
\n" ); document.write( "\n" ); document.write( " $\"%28R%5Bn%5D%2BR%5Bp%5D%29%2A3=100\"$
\n" ); document.write( "2. $\"R%5Bn%5D%2BR%5Bp%5D=100%2F3\"$
\n" ); document.write( ".
\n" ); document.write( ".\r
\n" ); document.write( "\n" ); document.write( " $\"%28R%5Bm%5D%2BR%5Bp%5D%29%2A2=100\"$
\n" ); document.write( "3. $\"R%5Bm%5D%2BR%5Bp%5D=50\"$
\n" ); document.write( "Substitute eq. 1 into eq. 3,
\n" ); document.write( " $\"25%2BR%5Bp%5D=50\"$
\n" ); document.write( " $\"R%5Bp%5D=25\"$
\n" ); document.write( "Now substitute this into eq. 2,
\n" ); document.write( " $\"R%5Bn%5D%2B25=100%2F3\"$
\n" ); document.write( " $\"R%5Bn%5D=100%2F3-75%2F3\"$
\n" ); document.write( " $\"R%5Bn%5D=25%2F3\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"R%5Bn%5D%2At%5Bn%5D=100\"$
\n" ); document.write( " $\"%2825%2F3%29%2At%5Bn%5D=100\"$
\n" ); document.write( " $\"t%5Bn%5D=12\"$ $\"hrs\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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