document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107438>Question 107438</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jim can fill a pool carrying buckets of water in 30 minutes.  Sue can do the same job in 45 minutes.  Tony can do the same job in 1 1/2 hours.  How quickly can all three fill the pool together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78216 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=78216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's one way of looking at the problem:<BR>\n" );
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document.write( "First, since Jim can fill the pool in 30 minutes, this means that for each minute he fills<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F30 ALIGN=MIDDLE  ALT=\"1%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the pool.<BR>\n" );
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document.write( "Next, since Sue can fill the pool in 45 minutes, this means that in one minute she fills<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F45 ALIGN=MIDDLE  ALT=\"1%2F45\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the pool.<BR>\n" );
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document.write( "Finally, since Tony can fill the pool in 90 minutes (90 minutes = 1 1/2 hours) for each minute<BR>\n" );
document.write( "he works, he fills <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F90 ALIGN=MIDDLE  ALT=\"1%2F90\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the pool.<BR>\n" );
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document.write( "Then for each minute that they work together their total contribution to filling the pool is <BR>\n" );
document.write( "the sum of their individual contributions ... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F30+%2B+1%2F45+%2B+1%2F90%29 ALIGN=MIDDLE  ALT=\"%281%2F30+%2B+1%2F45+%2B+1%2F90%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "90 is the least common denominator. Convert the fractions so they all have 90 as the denominator.<BR>\n" );
document.write( "When you do, the sum becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F30+%2B+1%2F45+%2B+1%2F90+=+3%2F90+%2B+2%2F90+%2B+1%2F90+=+6%2F90 ALIGN=MIDDLE  ALT=\"1%2F30+%2B+1%2F45+%2B+1%2F90+=+3%2F90+%2B+2%2F90+%2B+1%2F90+=+6%2F90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and 6 is a common factor of both the numerator and denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F90 ALIGN=MIDDLE  ALT=\"6%2F90\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Therefore,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F90+=+%286%2A1%29%2F%286%2A15%29+=+%28cross%286%29%2A1%29%2F%28cross%286%29%2A15%29+=+1%2F15 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This shows that when Jim, Sue, and Tony work together that each minute they fill <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F15 ALIGN=MIDDLE  ALT=\"1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the<BR>\n" );
document.write( "pool. Therefore, in 15 minutes they will fill the pool.<BR>\n" );
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document.write( "In equation form this becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F30+%2B+1%2F45%2B1%2F90%29%2AT+=+1 ALIGN=MIDDLE  ALT=\"%281%2F30+%2B+1%2F45%2B1%2F90%29%2AT+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "where the 1 on the right side represents 1 pool full and T is the unknown number of minutes<BR>\n" );
document.write( "that it takes to fill 1 pool.<BR>\n" );
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document.write( "When you combine the three fractions as we did previously this equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F15%29%2AT+=+1 ALIGN=MIDDLE  ALT=\"%281%2F15%29%2AT+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for T by either dividing both sides of this equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F15 ALIGN=MIDDLE  ALT=\"1%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > or by multiplying<BR>\n" );
document.write( "both sides by 15 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+15 ALIGN=MIDDLE  ALT=\"T+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "and since we were working in units of minutes, the answer for filling the pool when all <BR>\n" );
document.write( "three persons work together is T = 15 minutes.<BR>\n" );
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document.write( "Another way of looking at the problem is to find a common number of minutes that is divisible<BR>\n" );
document.write( "by 30, 45, and 90. That number is 90. Then look at it this way ... in 90 minutes Jim would<BR>\n" );
document.write( "fill the pool 3 times, Sue would fill it twice, and Tony would fill it once. Therefore, <BR>\n" );
document.write( "if all three worked together, they would fill the pool a total of 6 times in 90 minutes. So<BR>\n" );
document.write( "to find how long it takes to fill the pool once, divide 90 minutes by 6 times and you<BR>\n" );
document.write( "get 15 minutes ... the same answer as we got previously.<BR>\n" );
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document.write( "Hope this helps you to understand how to do the problem.<BR>\n" );
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document.write( " </SPAN>\n" );
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