document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=938665>Question 938665</A>: <I><SPAN STYLE=\"word-break: break-all;\"> one pipe can fill a pool in 6 hours. The drain can empty the whole pool in 12 hours. With the pipe and the drain open how long will it take the pool to be filled?\r<BR>\n" );
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document.write( "Mr.Poly Nomials takes 8 hours to paint his room. After working for one hour , he called in a painter to help him. Working together they finished the job 3 more hours. How long would it take the painter to finish the job if he had worked alone?<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 #571870 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=571870\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> one pipe can fill a pool in 6 hours. The drain can empty the whole pool in 12 hours. With the pipe and the drain open how long will it take the pool to be filled? \r<BR>\n" );
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document.write( " (1)<BR>\n" );
document.write( "Let x=time it takes to fill pool with both pipes open<BR>\n" );
document.write( "with both pipes open they fill at the rate of 1/x of the pool per hour<BR>\n" );
document.write( "Fill pipe fills at the rate of 1/6 of the pool per hour<BR>\n" );
document.write( "Drain pipe empties at the rate of 1/12 of the pool per hour<BR>\n" );
document.write( "So, our equation to solve is:<BR>\n" );
document.write( "(1/6)-(1/12)=(1/x) multiply each term by 12x<BR>\n" );
document.write( "2x-x=12<BR>\n" );
document.write( "x=12 hours <BR>\n" );
document.write( "CK<BR>\n" );
document.write( "In 12 hours, fill pipe fills (1/6)*12=2 pools<BR>\n" );
document.write( "In 12 hours, drain pipe drains (1/12)*12=1 pool<BR>\n" );
document.write( "So in twelve hours we have a net total of 1 pool filled:)\r<BR>\n" );
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document.write( "Mr.Poly Nomials takes 8 hours to paint his room. After working for one hour , he called in a painter to help him. Working together they finished the job 3 more hours. How long would it take the painter to finish the job if he had worked alone?\r<BR>\n" );
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document.write( "(2)<BR>\n" );
document.write( "Let x=amount of time it takes painter to paint the room<BR>\n" );
document.write( "And let t=time it takes painter to finish the room working alone <BR>\n" );
document.write( "So painter works at the rate of 1/x of the room per hour<BR>\n" );
document.write( "Poly works at the rate of 1/8 of the room per hour<BR>\n" );
document.write( "So after 1 hour poly paints 1/8 of the room, leaving 7/8 of the room yet to be painted<BR>\n" );
document.write( "So:<BR>\n" );
document.write( "(1/8)*3+(1/x)*3=7/8<BR>\n" );
document.write( "3/8 +3/x=7/8  multiply each term by 8x<BR>\n" );
document.write( "3x+24=7x<BR>\n" );
document.write( "4x=24<BR>\n" );
document.write( "x=6 hours amount of time it takes painter working alone to paint the whole room<BR>\n" );
document.write( "Now we know the painter paints at the rate of (1/6) room per hour<BR>\n" );
document.write( "Now our problem to solve is:<BR>\n" );
document.write( "(1/6)*t=7/8 multiply each term by 24<BR>\n" );
document.write( "4t=21<BR>\n" );
document.write( "t=21/4 =5 1/4 hours----Time it takes painter to finish the job working alone.\r<BR>\n" );
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document.write( "Does this help?---ptaylor\r<BR>\n" );
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