document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=414561>Question 414561</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One machine can turn out 1000 pieces in 12 days. A second machine takes 18 days to turn out 1000 pieces. On a particular run the first machine operated for 4 days alone. The second machine was then put into operation, and the two worked together. How long did it take to finish 1000 pieces </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #290849 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=290849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One machine can turn out 1000 pieces in 12 days.<BR>\n" );
document.write( " A second machine takes 18 days to turn out 1000 pieces.<BR>\n" );
document.write( " On a particular run the first machine operated for 4 days alone.<BR>\n" );
document.write( " The second machine was then put into operation, and the two worked together.<BR>\n" );
document.write( " How long did it take to finish 1000 pieces?<BR>\n" );
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document.write( "Let t = time that the two machines worked together<BR>\n" );
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document.write( "Let the completed job = 1 (1000 pieces made)<BR>\n" );
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document.write( "Mach 1 + Mach 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t%2B4%29%2F12 ALIGN=MIDDLE  ALT=\"%28t%2B4%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2F18 ALIGN=MIDDLE  ALT=\"t%2F18\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply eq by 26 to clear the denominators, results:<BR>\n" );
document.write( "3(t+4) + 2t = 36<BR>\n" );
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document.write( "3t + 12 + 2t = 36<BR>\n" );
document.write( "5t = 36 - 12<BR>\n" );
document.write( "5t = 24<BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F5 ALIGN=MIDDLE  ALT=\"24%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 4.8 days working together to finish the job<BR>\n" );
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document.write( "Check this: (Machine 1 worked 8.8 days)<BR>\n" );
document.write( "8.8/12 + 4.8/18 = <BR>\n" );
document.write( ".733 + .267 = 1.0 confirms our solution of 4.8 days working together<BR>\n" );
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