document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121892>Question 121892</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395535921/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Two harvesting machines can each harvest a field in 15 hrs. If they are joined by a newer machine and the three machines work together, the job takes 3 hrs. How long would it talk for the newer machine to harvest the field alone?\r<BR>\n" );
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document.write( "i have not a clue where to start...im so bad at story problems..i can do the problems and get algebra but i never know what to do with story problems and how to set them up?<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 #89571 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=89571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two harvesting machines can each harvest a field in 15 hrs. If they are joined by a newer machine and the three machines work together, the job takes 3 hrs. How long would it take for the newer machine to harvest the field alone?<BR>\n" );
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document.write( "Let x = the time the newer machine needs to complete the job alone<BR>\n" );
document.write( "Let the completed job = 1<BR>\n" );
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document.write( "Each machine will do a fraction of the work<BR>\n" );
document.write( "All three will work for 3 hrs so we can say:<BR>\n" );
document.write( "Each original machine will 3/15<BR>\n" );
document.write( "The new machine: 3/x <BR>\n" );
document.write( "Remember the completed job = 1:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F15 ALIGN=MIDDLE  ALT=\"3%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F15 ALIGN=MIDDLE  ALT=\"3%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fx ALIGN=MIDDLE  ALT=\"3%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "we can simplify this the 1st two machine = 6/15 reduced to 2/5<BR>\n" );
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document.write( "Now we have a real simple equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fx ALIGN=MIDDLE  ALT=\"3%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
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document.write( "Multiply the equation by 5x to get rid of the denominators<BR>\n" );
document.write( "5x*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 5x<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fx ALIGN=MIDDLE  ALT=\"3%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5x(1)<BR>\n" );
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document.write( "Cancel out the denominators and we have:<BR>\n" );
document.write( "2x + 15 = 5x<BR>\n" );
document.write( "15 = 5x = 2x<BR>\n" );
document.write( "15 = 3x<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F3 ALIGN=MIDDLE  ALT=\"15%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 5 hrs for the new machine to do it alone.<BR>\n" );
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document.write( "Check solution in the original equation<BR>\n" );
document.write( "3/15 + 3/15 + 3/5 =<BR>\n" );
document.write( "1/5 + 1/5 + 3/5 = 1; confirms our solution<BR>\n" );
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document.write( "Hopefully this provided a few clues, did it make sense to you? Any questions? <BR>\n" );
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