document.write( "Question 737075: It takes Billy 2 hours to do a certain job than it takes Reena. They worked together for 2 hours; then Reena left, and Billy finished the job in 1 hour. How long would it take each of them to do the job alone? \n" ); document.write( "

Algebra.Com's Answer #450164 by lwsshak3(11628) $\"\"$ $\"About$

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It takes Billy 2 hours to do a certain job than it takes Reena. They worked together for 2 hours; then Reena left, and Billy finished the job in 1 hour. How long would it take each of them to do the job alone?
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\n" ); document.write( "let x=time it takes Reena to do the job alone
\n" ); document.write( "1/x=Her work rate
\n" ); document.write( "(x+2)=time it takes Billy to do the job alone
\n" ); document.write( "1/(x+2)=His work rate
\n" ); document.write( "Work done=time on job*work rate
\n" ); document.write( " $\"2%2Fx%2B2%2F%28x%2B2%29%2B1%2F%28x%2B2%29=1\"$
\n" ); document.write( " $\"2%2Fx%2B3%2F%28x%2B2%29=1\"$
\n" ); document.write( "LCD:x(x+2)
\n" ); document.write( "2(x+2)+3x=x(x+2)
\n" ); document.write( "2x+4+3x=x^2+2x
\n" ); document.write( "x^2-3x-4=0
\n" ); document.write( "(x-4)(x+1)=0
\n" ); document.write( "x=-1 (reject)
\n" ); document.write( "x=4
\n" ); document.write( "x+2=6
\n" ); document.write( "time it takes Reena to do the job alone=4 hrs
\n" ); document.write( "time it takes Billy to do the job alone=6 hrs \n" ); document.write( "

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