document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72718>Question 72718</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395430526/algebrahomeworkh>Algebra:Structure and Method</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> One computer can process a payroll in 60 minutes. A newer computer can process a payroll in 40 minutes. How long would it take to process the payroll if both computers worked together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51994 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=51994\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One way to look at this is that in 1 minute the first computer does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F60 ALIGN=MIDDLE  ALT=\"1%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job.<BR>\n" );
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document.write( "And in the same time (1 minute) the new computer does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F40 ALIGN=MIDDLE  ALT=\"1%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job.<BR>\n" );
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document.write( "Stop and think about this a little. It'll help to make sense of this problem.  If the first<BR>\n" );
document.write( "computer runs for 30 minutes, how much of the job will it complete? Just multiply the 30 minutes<BR>\n" );
document.write( "times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F60 ALIGN=MIDDLE  ALT=\"1%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F60 ALIGN=MIDDLE  ALT=\"30%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this reduces to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So if it takes 60<BR>\n" );
document.write( "minutes to complete the entire job, in 30 minutes it will be half done.  Now think about what<BR>\n" );
document.write( "we did to find this out.  We multiplied the Rate which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F60 ALIGN=MIDDLE  ALT=\"1%2F60\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job per each<BR>\n" );
document.write( "minute times the number of minutes.  The same sort of thinking could be done for the second<BR>\n" );
document.write( "(newer) computer.  It completes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F40 ALIGN=MIDDLE  ALT=\"1%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job each minute and by multiplying<BR>\n" );
document.write( "this rate by the number of minutes it operates, you can determine how much of the job it<BR>\n" );
document.write( "has completed. In the same 30 minutes as the first machine it would do<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F40%29%2A30+=+30%2F40+=+3%2F4 ALIGN=MIDDLE  ALT=\"%281%2F40%29%2A30+=+30%2F40+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "or three-quarters of the job. Obviously, 30 minutes is too much time because the two machines<BR>\n" );
document.write( "working together complete one-half plus three- quarters of the job in 30 minutes or more<BR>\n" );
document.write( "than the entire job.<BR>\n" );
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document.write( "So in each case let's multiply the elapsed time by the rate for the computer and when you<BR>\n" );
document.write( "add the two computer outputs together it should equal 1 job done.  In equation form this<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F60%29%2At+%2B+%281%2F40%29%2At+=+1 ALIGN=MIDDLE  ALT=\"%281%2F60%29%2At+%2B+%281%2F40%29%2At+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where t represents the time from the start when the two computers began working on the job.<BR>\n" );
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document.write( "If you factor the t from the two terms on the left side of this equation you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2A%28%281%2F60%29+%2B+%281%2F40%29%29+=+1 ALIGN=MIDDLE  ALT=\"t%2A%28%281%2F60%29+%2B+%281%2F40%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A common denominator for the two fractions is 120.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F60+=+2%2F120 ALIGN=MIDDLE  ALT=\"1%2F60+=+2%2F120\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F40+=+3%2F120 ALIGN=MIDDLE  ALT=\"1%2F40+=+3%2F120\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "so that when you add these two you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B2%29%2F120+=+5%2F120%29 ALIGN=MIDDLE  ALT=\"%283%2B2%29%2F120+=+5%2F120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "The equation then becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2A%285%2F120%29+=+1 ALIGN=MIDDLE  ALT=\"t%2A%285%2F120%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can now solve the equation either by dividing both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F120 ALIGN=MIDDLE  ALT=\"5%2F120\"   DISABLED_style= \"max-width:90%; height:auto;\" > or by multiplying<BR>\n" );
document.write( "both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2F5 ALIGN=MIDDLE  ALT=\"120%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "When you do that the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28120%2F5%29 ALIGN=MIDDLE  ALT=\"t+=+%28120%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "and dividing 5 into 120 results in an answer of 24.  So 24 minutes is the amount of processing<BR>\n" );
document.write( "time it will take both machines working together to do 1 payroll.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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