document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76431>Question 76431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To empty their swimming pool, the Johnsons decided to use the regular drain and pump. If it takes 15 hours for the pool to empty using the drain alone and 7 hours for the pool to empty using the pump alone, how long will it take for the pool to empty using both the drain and the pump?\r<BR>\n" );
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document.write( "?  hours<BR>\n" );
document.write( "(round to the nearest0.1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54817 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=54817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If it takes 15 hours to empty the pool alone by using the drain, then one-fifteenth <BR>\n" );
document.write( "of the pool is emptied each hour that the drain is open. <BR>\n" );
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document.write( "If it takes 7 hours for the pump alone to empty the pool, then one-seventh of the pool is<BR>\n" );
document.write( "emptied each hour that the pump is on.<BR>\n" );
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document.write( "If the drain and the pump are both opened for t hours, then the pool is emptied and the <BR>\n" );
document.write( "1 job of pool emptying is complete.  In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F15%29%2At+%2B+%281%2F7%29%2At+=+1 ALIGN=MIDDLE  ALT=\"%281%2F15%29%2At+%2B+%281%2F7%29%2At+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiplying all these terms (both sides) by 15*7 eliminates the denominators and results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7t+%2B+15t+=+7%2A15 ALIGN=MIDDLE  ALT=\"7t+%2B+15t+=+7%2A15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add the two terms on the left side and multiply out the right side to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22t+=+105 ALIGN=MIDDLE  ALT=\"22t+=+105\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "At this point you can solve for t by dividing both sides of the equation by 22 and this<BR>\n" );
document.write( "results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+105%2F22+=+4.77272727... ALIGN=MIDDLE  ALT=\"+t+=+105%2F22+=+4.77272727...\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours<BR>\n" );
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document.write( "Rounding this to the nearest tenth of an hour says that the pump and drain will empty the<BR>\n" );
document.write( "pool in 4.8 hours.<BR>\n" );
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document.write( "Hope this helps.  The critical parts of the problem involve finding the individual rates <BR>\n" );
document.write( "for the pump and the drain, recognizing that each of these rates times the common time that<BR>\n" );
document.write( "the two methods of draining are operating together represents the combined amount of <BR>\n" );
document.write( "drainage, and understanding that the combined amount of drainage is equal to 1 ... the <BR>\n" );
document.write( "one job is completed.<BR>\n" );
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