document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=360906>Question 360906</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A would takes 6 hours to paint a wall working alone.  B takes 4 hours. C 3 hours<BR>\n" );
document.write( "A starts painting at noon, at 1.00 pm B joins him, C at 1.30 pm. At what time do they finish the painting ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #257500 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20063)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=257500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A would takes 6 hours to paint a wall working alone.  B takes 4 hours. C 3 hours<BR>\n" );
document.write( "A starts painting at noon, at 1.00 pm B joins him, C at 1.30 pm. At what time do they finish the painting ?<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Let t = the time in hours after 1:30PM until the painting is finished.\r\n" );
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document.write( "Make this chart and fill in t for the time after 1:30PM until the painting\r\n" );
document.write( "is done.\r\n" );
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document.write( "                      Walls painted  | Time | Rate in Walls/hour\r\n" );
document.write( "A working alone     |                |      |\r\n" );
document.write( "B working alone     |                |      |\r\n" );
document.write( "C working alone     |                |      | \r\n" );
document.write( "A from 12 to 1PM    |                |      |\r\n" );
document.write( "A&B from 1 to 1:30PM|                |      | \r\n" );
document.write( "A&B&C after 1:30PM  |                |  t   | \r\n" );
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document.write( "</PRE><BR>\n" );
document.write( ">>...A would takes 6 hours to paint a wall working alone.  <BR>\n" );
document.write( "     B takes 4 hours. C 3 hours...<<<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Fill in the times for A, B, and C and 1 for the number of walls painted\r\n" );
document.write( "in those times.\r\n" );
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document.write( "                      Walls painted  | Time | Rate in Walls/hour\r\n" );
document.write( "A working alone     |       1        |  6   |\r\n" );
document.write( "B working alone     |       1        |  4   |\r\n" );
document.write( "C working alone     |       1        |  3   | \r\n" );
document.write( "A from 12 to 1PM    |                |      |\r\n" );
document.write( "A&B from 1 to 1:30PM|                |      | \r\n" );
document.write( "A&B&C after 1:30PM  |                |  t   | \r\n" );
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document.write( "Next fill in the Walls/hour rates for A, B and C individually, by \r\n" );
document.write( "dividing their number of walls painted, which is 1, by their times\r\n" );
document.write( "in hours to paint 1 wall working alone:\r\n" );
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document.write( "                      Walls painted  | Time | Rate in Walls/hour\r\n" );
document.write( "A working alone     |       1        |  6   |        1/6\r\n" );
document.write( "B working alone     |       1        |  4   |        1/4\r\n" );
document.write( "C working alone     |       1        |  3   |        1/3\r\n" );
document.write( "A from 12 to 1PM    |                |      |\r\n" );
document.write( "A&B from 1 to 1:30PM|                |      | \r\n" );
document.write( "A&B&C after 1:30PM  |                |  t   | \r\n" );
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document.write( "Fill in A's rate of 1/6 walls/hour also when he paints from 12 noon to 1PM\r\n" );
document.write( "and 1 hour for the time:\r\n" );
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document.write( "                      Walls painted  | Time | Rate in Walls/hour\r\n" );
document.write( "A working alone     |       1        |  6   |        1/6\r\n" );
document.write( "B working alone     |       1        |  4   |        1/4\r\n" );
document.write( "C working alone     |       1        |  3   |        1/3\r\n" );
document.write( "A from 12 to 1PM    |                |  1   |        1/6 \r\n" );
document.write( "A&B from 1 to 1:30PM|                |      | \r\n" );
document.write( "A&B&C after 1:30PM  |                |  t   | \r\n" );
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document.write( "Add A's rate and B's rate to find their combined rate:\r\n" );
document.write( "1/6 + 1/4 = 2/12 + 3/12 = 5/12 and 1/2 hour for their time working\r\n" );
document.write( "together from 1PM to 1:30PM\r\n" );
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document.write( "                      Walls painted  | Time | Rate in Walls/hour\r\n" );
document.write( "A working alone     |       1        |  6   |        1/6\r\n" );
document.write( "B working alone     |       1        |  4   |        1/4\r\n" );
document.write( "C working alone     |       1        |  3   |        1/3\r\n" );
document.write( "A from 12 to 1PM    |                |  1   |        1/6 \r\n" );
document.write( "A&B from 1 to 1:30PM|                | 1/2  |       5/12  \r\n" );
document.write( "A&B&C after 1:30PM  |                |  t   | \r\n" );
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document.write( "Add A's, B's and C's rate to find the combined rate for all three\r\n" );
document.write( "after 1:30PM\r\n" );
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document.write( "1/6 + 1/4 + 1/3 = 2/12 + 3/12 + 4/12 = 9/12 = 3/4\r\n" );
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document.write( "                      Walls painted  | Time | Rate in Walls/hour\r\n" );
document.write( "A working alone     |       1        |  6   |        1/6\r\n" );
document.write( "B working alone     |       1        |  4   |        1/4\r\n" );
document.write( "C working alone     |       1        |  3   |        1/3\r\n" );
document.write( "A from 12 to 1PM    |                |  1   |        1/6 \r\n" );
document.write( "A&B from 1 to 1:30PM|                | 1/2  |       5/12  \r\n" );
document.write( "A&B&C after 1:30PM  |                |  t   |        3/4\r\n" );
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document.write( "Fill in the fraction of a wall painted by A alone from 12 noon to 1PM\r\n" );
document.write( "by multiplying his rate times his time: (1/6)(1) = 1/6\r\n" );
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document.write( "                      Walls painted  | Time | Rate in Walls/hour\r\n" );
document.write( "A working alone     |       1        |  6   |        1/6\r\n" );
document.write( "B working alone     |       1        |  4   |        1/4\r\n" );
document.write( "C working alone     |       1        |  3   |        1/3\r\n" );
document.write( "A from 12 to 1PM    |      1/6       |  1   |        1/6 \r\n" );
document.write( "A&B from 1 to 1:30PM|                | 1/2  |       5/12  \r\n" );
document.write( "A&B&C after 1:30PM  |                |  t   |        3/4\r\n" );
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document.write( "Fill in the fraction of a wall painted by A&B from 1PM to 1:30PM\r\n" );
document.write( "by multiplying their combined rate times their time: (1/2)(5/12) = 5/24\r\n" );
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document.write( "                      Walls painted  | Time | Rate in Walls/hour\r\n" );
document.write( "A working alone     |       1        |  6   |        1/6\r\n" );
document.write( "B working alone     |       1        |  4   |        1/4\r\n" );
document.write( "C working alone     |       1        |  3   |        1/3\r\n" );
document.write( "A from 12 to 1PM    |      1/6       |  1   |        1/6 \r\n" );
document.write( "A&B from 1 to 1:30PM|     5/24       | 1/2  |       5/12  \r\n" );
document.write( "A&B&C after 1:30PM  |   (3/4)t       |  t   |        3/4\r\n" );
document.write( "\r\n" );
document.write( "Fill in the fraction of a wall painted by A&B&C after 1:30PM\r\n" );
document.write( "by multiplying their combined rate times their time: (3/4)t \r\n" );
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document.write( "    The equation is obtained by adding the three fractions\r\n" );
document.write( "    of a wall painted beginning at 12 noon, and setting that\r\n" );
document.write( "    sum equal to 1 wall:\r\n" );
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document.write( "            1/6 + 5/24 + (3/4)t = 1\r\n" );
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document.write( "Clear of fractions by multiplying through by 24:\r\n" );
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document.write( "                    4 + 5 + 18t = 24\r\n" );
document.write( "                        9 + 18t = 24\r\n" );
document.write( "                            18t = 15\r\n" );
document.write( "                              t = 15/18\r\n" );
document.write( "                              t = 5/6 of an hour\r\n" );
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document.write( "5/6 of an hour is (5/6)(60) = 50 minutes.  So the painting was \r\n" );
document.write( "finished at 50 minutes after 1:30PM or 2:20PM.\r\n" );
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document.write( "Edwin</PRE>       </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );