document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=265496>Question 265496</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am doing a practice exam for my GRE and I am stumped on this type of problem. Can you help?\r<BR>\n" );
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document.write( "3. 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 ½ hours. How quickly can all three fill the pool together? \r<BR>\n" );
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document.write( "A. 12 minutes <BR>\n" );
document.write( "B. 15 minutes <BR>\n" );
document.write( "C. 21 minutes <BR>\n" );
document.write( "D. 23 minutes <BR>\n" );
document.write( "E. 28 minutes<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 #195225 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=195225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = units\r<BR>\n" );
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document.write( "this translates to:\r<BR>\n" );
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document.write( "number of units produced per minute * number of minutes = number of units produced.\r<BR>\n" );
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document.write( "the number of units produced is 1 full pool.\r<BR>\n" );
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document.write( "jim can fill the pool in 30 minutes which means jim can fill 1/30 of the pool each minute.\r<BR>\n" );
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document.write( "1/30 * 30 = 1\r<BR>\n" );
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document.write( "sue can fill the pool in 45 minutes which means sue can fill 1/45 of the pool each minute.\r<BR>\n" );
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document.write( "1/45 * 45 = 1\r<BR>\n" );
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document.write( "tony can fill the pool in 1 and 1/2 hours which means that tony can fill the pool in 90 minutes which means that tony can fill 1/90 of the pool each minute.\r<BR>\n" );
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document.write( "1/90 * 90 = 1\r<BR>\n" );
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document.write( "when they work together, their combined rates are additive.\r<BR>\n" );
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document.write( "if we let x = the number of minutes it takes to fill the pool, then we have:\r<BR>\n" );
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document.write( "rate * x = 1\r<BR>\n" );
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document.write( "the combined rate is equal to jim's rate plus sue's rate plus tony's rate.\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "(1/30 + 1/45 + 1/90) * x = 1\r<BR>\n" );
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document.write( "1/30 + 1/45 + 1/90 = 3/90 + 2/90 + 1/90 = 6/90 = 1/15.\r<BR>\n" );
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document.write( "their combined rate is 1/15 of the pool every minute.\r<BR>\n" );
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document.write( "formula becomes:\r<BR>\n" );
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document.write( "1/15 * x = 1\r<BR>\n" );
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document.write( "multiply both sides of this equation by 15 to get:\r<BR>\n" );
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document.write( "x = 15\r<BR>\n" );
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document.write( "working together, they will take 15 minutes to fill the pool.\r<BR>\n" );
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document.write( "in 15 minutes jim has filled 1/30 * 15 = 15/30 = 1/2 of the pool.\r<BR>\n" );
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document.write( "in the same 15 minutes, sue has filled 1/45 * 15 = 1/3 of the pool.\r<BR>\n" );
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document.write( "in the same 15 minutes, tony has filled 1/90 * 15 = 1/6 of the pool.\r<BR>\n" );
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document.write( "1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 1 full pool.\r<BR>\n" );
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document.write( "your answer is selection B (15 minutes).\r<BR>\n" );
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