document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388218>Question 388218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> here is another tricky question.\r<BR>\n" );
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document.write( "On a certain day two inspectors, A and B, employed by a factory, were inspecting a lot of manufactured articles. In the morning A ha inspected 1500 articles before B started in. during the remainder of the morning they inspected 4000 more, A working 4 hours altogether. In the afternoon A worked 4 hrs. and B 2 hrs., in which time they inspected 5200 articles. Find the average number of articles that each inspected per hour and the number of hrs. that B worked in the morning.<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 #274706 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=274706\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Okay this is what I got:<BR>\n" );
document.write( "let a = articles/hr done by A<BR>\n" );
document.write( "b = articles/hr done by B.<BR>\n" );
document.write( "Let x = # hrs done by A in the morning BEFORE B joined him.<BR>\n" );
document.write( "Then:<BR>\n" );
document.write( "ax = 1500  <------(1)<BR>\n" );
document.write( "(a+b)(4-x) = 4000 <------(2) <BR>\n" );
document.write( "4a + 2b = 5200, which is the same as    2a + b = 2600<---(3)<BR>\n" );
document.write( "We got a system of non-linear equations.<BR>\n" );
document.write( "From eq'n (3),  b = 2600 - 2a<BR>\n" );
document.write( "From eq'n(1), x = 1500/a.  Plugging both of these into (2), we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B2600-2a%29%284+-+1500%2Fa%29+=+4000 ALIGN=MIDDLE  ALT=\"%28a%2B2600-2a%29%284+-+1500%2Fa%29+=+4000\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282600+-+a%29%284-1500%2Fa%29+=+4000 ALIGN=MIDDLE  ALT=\"%282600+-+a%29%284-1500%2Fa%29+=+4000\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10400-+3900000%2Fa+-+4a+%2B+1500+=+4000 ALIGN=MIDDLE  ALT=\"10400-+3900000%2Fa+-+4a+%2B+1500+=+4000\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3900000%2Fa+-+4a+=+-7900 ALIGN=MIDDLE  ALT=\"-3900000%2Fa+-+4a+=+-7900\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=975000%2Fa%2Ba+=+1975 ALIGN=MIDDLE  ALT=\"975000%2Fa%2Ba+=+1975\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is equivalent to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-+1975a%2B975000+=+0 ALIGN=MIDDLE  ALT=\"a%5E2-+1975a%2B975000+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > after multiplying both sides by a and transposition.<BR>\n" );
document.write( "(a - 1000)(a - 975) = 0----> a = 1000, or 975.\r<BR>\n" );
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document.write( "If a = 1000, b = 600, and x = 1.5 hrs.<BR>\n" );
document.write( "If a = 975, b = 650, and x = 20/13 hrs.\r<BR>\n" );
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document.write( "So we actually have 2 possible scenarios here, both being viable.<BR>\n" );
document.write( "B worked for 4 - x = 4 - 1.5 = 2.5 hours in the morning, OR, equally possible,<BR>\n" );
document.write( "4 - 20/13 = 32/13 hours in the morning. </SPAN>\n" );
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