document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75818>Question 75818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An old-model machine can stamp 1000 parts in 4 hours. A new-model machine can stamp 1000 parts in just two hours. How long will it take both machines to stamp 1000 parts working together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54444 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=54444\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One way to look at this problem is to determine the hourly rate of stamping parts for each<BR>\n" );
document.write( "of the machines.<BR>\n" );
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document.write( "The old machine stamps out 1000 parts in 4 hours.  That means that each hour it stamps<BR>\n" );
document.write( "out 250 parts (1000 divided by 4).  The new machine stamps out 1000 parts in 2 hours and<BR>\n" );
document.write( "that means that it stamps at the rate of 500 parts per hour (1000 divided by 2).<BR>\n" );
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document.write( "If t represents the time that both machines are stamping together, then we just multiply <BR>\n" );
document.write( "the rates of the two machines by t to get the output, and we need that output to be 1000 parts.<BR>\n" );
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document.write( "Does this make sense to you? Think of it this way ... if the machines work together for<BR>\n" );
document.write( "one hour, the old machine produces 250 parts and the new machine produces 500 parts.<BR>\n" );
document.write( "So together they have produced 750 parts.  But we need 1000 parts.  Suppose we let the<BR>\n" );
document.write( "two machines work together for 2 hours.  The old machine produces 250*2 or 500 parts and<BR>\n" );
document.write( "the new machine produces 500*2 = 1000 parts.  So in the 2 hours the combined output of<BR>\n" );
document.write( "the two machines is 1500 parts ... more than we need. <BR>\n" );
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document.write( "The way to find the exact time needed is to multiply the unknown time, t, by each of<BR>\n" );
document.write( "the rates of the two machines and set the answer equal to 1000. 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=250%2At+%2B+500%2At+=+1000 ALIGN=MIDDLE  ALT=\"250%2At+%2B+500%2At+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Add the two terms on the left and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=750%2At+=+1000 ALIGN=MIDDLE  ALT=\"750%2At+=+1000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now divide both sides by 750 to find that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1000%2F750+=+1.333333 ALIGN=MIDDLE  ALT=\"t+=+1000%2F750+=+1.333333\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the production time to produce 1000 parts is 1.333333 hrs or 1 hr and 20 minutes <BR>\n" );
document.write( "(a third of an hour is 20 minutes).<BR>\n" );
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document.write( "Hope this helps you to understand a little better a method for working work-rates <BR>\n" );
document.write( "problems. </SPAN>\n" );
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