document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=357297>Question 357297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A team of 4 people has just finished half of a project in 10 days. If the rest of the project needs to be done in 5 more days, how many more people are needed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #255165 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=255165\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the assumption is that they all work at the same rate.\r<BR>\n" );
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document.write( "right off the bat, i would say 8 people would be required.\r<BR>\n" );
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document.write( "that's because twice as many people should be able to do the same work in half the time assuming that they all work at the same rate.\r<BR>\n" );
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document.write( "a more formal approach would be as follows;\r<BR>\n" );
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document.write( "Rate * Time = Units\r<BR>\n" );
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document.write( "The number of units is equal to 1 (the project).\r<BR>\n" );
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document.write( "Since half the project was finished, then Units = .5\r<BR>\n" );
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document.write( "Since the time it took was 10 days, then Time = 10\r<BR>\n" );
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document.write( "The formula becomes Rate * 10 = .5\r<BR>\n" );
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document.write( "Divide both sides of this equation by 10 to get Rate = .5/10 which becomes:\r<BR>\n" );
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document.write( "Rate = .05 units per day.\r<BR>\n" );
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document.write( "This means that 4 people work at the the rate of .05 of the project per day.\r<BR>\n" );
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document.write( "10 * .05 = .5 which means that in 10 days 4 people finished half the project.\r<BR>\n" );
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document.write( "if you divide the rate of 4 people by 4, then you get the rate of 1 person.\r<BR>\n" );
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document.write( "the rate of 1 person becomes .05/4 = .125 of the project per day.\r<BR>\n" );
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document.write( "The question is how many people are required to finish the project in another 5 days.\r<BR>\n" );
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document.write( "the same formula applies.\r<BR>\n" );
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document.write( "rate * time = units\r<BR>\n" );
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document.write( "number of units = .5 (the other half of the project)<BR>\n" );
document.write( "time = 5 (the number of days required to finish the project).\r<BR>\n" );
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document.write( "the formula becomes:\r<BR>\n" );
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document.write( "rate * 5 = .5\r<BR>\n" );
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document.write( "divide both sides of the equation by 5 to get:\r<BR>\n" );
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document.write( "rate = .5/5 = .1\r<BR>\n" );
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document.write( "this means that .1 of the project needs to finished each day.\r<BR>\n" );
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document.write( "the rate of each person is .125 of the project per day.\r<BR>\n" );
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document.write( "multiply that by 8 and you get .1 of the project per day because 8 * .125 = 1.\r<BR>\n" );
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document.write( "8 persons are required to finished the project in another 5 days.\r<BR>\n" );
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document.write( "the combined rate of the people is additive.\r<BR>\n" );
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document.write( "if 1 person can do 1/2 of the project in one day and another person can do 1/2 of the project in 1 day, then both people will be able to complete the project in 1 day.   each person working alone would take 2 days.\r<BR>\n" );
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document.write( "same concept applies to this problem.\r<BR>\n" );
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document.write( "each person can finish .125 of the project in one day.<BR>\n" );
document.write( "8 persons can finish .1 of the project in one day.<BR>\n" );
document.write( "5 days total are required.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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