document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129133>Question 129133</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One printer can print the paychecks for the employees of a company in 54 min. A second printer can print the checks in 81 min. How long would it take to print the checks with both printers operating? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94392 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=94392\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the first printer can print all the checks in 54 minutes, then each minute it prints<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F54 ALIGN=MIDDLE  ALT=\"1%2F54\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the checks. So all you have to do is multiply this rate and you can find the<BR>\n" );
document.write( "number of checks it has printed. For example, in 5 minutes this printer will print <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A1%2F54+=+5%2F54 ALIGN=MIDDLE  ALT=\"5%2A1%2F54+=+5%2F54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So in 5 minutes this printer would print 5 fifty-fourths of the checks.  And in t minutes this<BR>\n" );
document.write( "printer will print <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2A%281%2F54%29+=+t%2F54 ALIGN=MIDDLE  ALT=\"t%2A%281%2F54%29+=+t%2F54\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the checks.<BR>\n" );
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document.write( "Similarly the each minute that goes by the other printer prints <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F81 ALIGN=MIDDLE  ALT=\"1%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the checks and<BR>\n" );
document.write( "in t minutes the other printer prints <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F81 ALIGN=MIDDLE  ALT=\"t%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the checks.<BR>\n" );
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document.write( "You can now add these two amounts of check printing together and set them equal to the 1 entire<BR>\n" );
document.write( "job. So you have the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F54+%2B+t%2F81+=+1 ALIGN=MIDDLE  ALT=\"t%2F54+%2B+t%2F81+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can get rid of the denominators by first multiplying both sides of this equation (all<BR>\n" );
document.write( "terms) by 54. When you multiply each term by 54 you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+%2B+54t%2F81+=+54 ALIGN=MIDDLE  ALT=\"t+%2B+54t%2F81+=+54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next get rid of the other denominator by multiplying both sides of this equation (all terms) <BR>\n" );
document.write( "by 81 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81t+%2B+54t+=+54%2A81 ALIGN=MIDDLE  ALT=\"81t+%2B+54t+=+54%2A81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side add the two terms to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=135t+=+54%2A81 ALIGN=MIDDLE  ALT=\"135t+=+54%2A81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And multiply out the right side to make the equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=135t+=+4374 ALIGN=MIDDLE  ALT=\"135t+=+4374\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 135 and you find that the equation is reduced to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+4374%2F135+=+32.4 ALIGN=MIDDLE  ALT=\"t+=+4374%2F135+=+32.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So when both printers work together, they can complete all the payroll checks in 32.4 minutes.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how to work it. <BR>\n" );
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