document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=551349>Question 551349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ~Working together a man and woman can do the job in 8 hours. if either had to do it alone, it would take a woman 2 hours longer than a man. How long would it take either person working alone?<BR>\n" );
document.write( "~A reservoir can be filled by one pipe in 6 hours and by another in 8 hours. It can be emptied by a third pipe in 10 hours. Starting empty, how long will it take to fill the reservoir if all pipes are open?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #359671 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=359671\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let Man take x hours to complete the job alone<BR>\n" );
document.write( "so he does 1/x of the job in 1 hour\r<BR>\n" );
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document.write( "woman takes 1/(x+2) hours to do the same job<BR>\n" );
document.write( "so she does 1/(x+2) of the job in 1 hour\r<BR>\n" );
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document.write( "Together they can do 1/x + 1/(x+2) of the job in 1 hour<BR>\n" );
document.write( "add up both<BR>\n" );
document.write( "=(2x+2)/x(x+2) \r<BR>\n" );
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document.write( "so they take x(x+2)/(2x+2) hours\r<BR>\n" );
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document.write( "x(x+2)/(2x+2)= 10<BR>\n" );
document.write( "x(x+2)=10(2x+2)<BR>\n" );
document.write( "x^2+2x=20x+20<BR>\n" );
document.write( "x^2-18x-20=0<BR>\n" );
document.write( "x^2-20x+2x-20=0<BR>\n" );
document.write( "x(x-20)+2(x-20)=0<BR>\n" );
document.write( "(x-20)(x+2)=0<BR>\n" );
document.write( "Take the positive value<BR>\n" );
document.write( "x= 20 \r<BR>\n" );
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document.write( "Man takes 20 hours<BR>\n" );
document.write( "Woman takes 20 +2 = 22 hours<BR>\n" );
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document.write( "1/6 +1/8 - 1/10 is the job done in 1 hour ( filling the pool)<BR>\n" );
document.write( "7/24 - 1/10<BR>\n" );
document.write( "Addup<BR>\n" );
document.write( "(70-24)/240<BR>\n" );
document.write( "46/240 of the job is done in 1 hour<BR>\n" );
document.write( "so it will take 240/46 hours = 5.2 hours\r<BR>\n" );
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document.write( "HAPPY NEW YEAR\r<BR>\n" );
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