document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=3198>Question 3198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Derek rakes and bags the leaves of a lawn in 3 hrs. Alferd rakes and bags them in 5 hours. How long will it take to rake and bag the leaves if they do it together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1376 by </B><A HREF=/tutors/aboutme.mpl?userid=drglass><B>drglass(89)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drglass><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=1376\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve this problem, you need to identify two things: <u>the form of the answer and the facts you have to solve the problem.</u><br><BR>\n" );
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document.write( "Form of the answer:<br><BR>\n" );
document.write( "The question is asking for the time it would take Derek and Alferd to rake the lawn and bag the leaves, so the answer should look like:<br>\r<BR>\n" );
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document.write( "   It would take them _____ hours to rake the lawn and bag the leaves.<br>\r<BR>\n" );
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document.write( "To make this easier to write, we will treat raking and bagging as one thing, but when we answer the question, we have to remember to include both parts.<br>\r<BR>\n" );
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document.write( "Facts:<BR>\n" );
document.write( "1) It takes Derek 3 hours to rake the lawn<BR>\n" );
document.write( "2) It takes Alferd 5 hours to rake the lawn<br>\r<BR>\n" );
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document.write( "Next, we write the facts in a mathematical way:<br>\r<BR>\n" );
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document.write( "Let's let the the letter D mean \"the speed at which Derek can rake the lawn\" so<br><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+%281+lawn%29%2F%283+hours%29 ALIGN=MIDDLE  ALT=\"D+=+%281+lawn%29%2F%283+hours%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "means Derek can rake <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > lawns per hour<br><BR>\n" );
document.write( "We can also let A mean \"the speed at which Alferd can rake the lawn,\" so<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+1%2F5 ALIGN=MIDDLE  ALT=\"A+=+1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > lawns per hour.<br>\r<BR>\n" );
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document.write( "Notice that the facts don't relate directly to the problem. They tell us about speed but not time. This makes it a little more difficult to solve because we have to hope we can relate speed to time. Fortunately, we can do exactly that.<br><BR>\n" );
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document.write( "With our facts written in a mathematical way, we can solve the problem.<br> \"The speed at which  Derek and Alferd can rake the lawn\" is written <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+D ALIGN=MIDDLE  ALT=\"A+%2B+D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.So our solution begins<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+D+=+%281%2F3%29+%2B+%281%2F5%29 ALIGN=MIDDLE  ALT=\"A+%2B+D+=+%281%2F3%29+%2B+%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > lawns per hour<br>\r<BR>\n" );
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document.write( "We make both fractions take the same denominator by multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F5 ALIGN=MIDDLE  ALT=\"5%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F3 ALIGN=MIDDLE  ALT=\"3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This gives us<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+%2B+D+=+%285%2F5%29%281%2F3%29+%2B+%283%2F3%29%281%2F5%29+=+%285%2F15%29+%2B+%283%2F15%29+=+%285+%2B+3%29%2F15+=+8%2F15 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > lawns per hour<hr>\r<BR>\n" );
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document.write( "This almost answers the question. It tells us that Derek and Alferd can rake <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F15 ALIGN=MIDDLE  ALT=\"8%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" > lawns per hour but, we need to know the time it takes them to rake one lawn. Let's call this time t.We can write this mathematically:<br>\r<BR>\n" );
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document.write( "1 lawn raked = (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F15%29 ALIGN=MIDDLE  ALT=\"8%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >lawns per hour) * (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours)<br>\r<BR>\n" );
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document.write( "If we divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F15 ALIGN=MIDDLE  ALT=\"8%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%288%2F15%29 ALIGN=MIDDLE  ALT=\"1%2F%288%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lawns%2F%28lawns%2Fhour%29 ALIGN=MIDDLE  ALT=\"lawns%2F%28lawns%2Fhour%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = t hours<br>\r<BR>\n" );
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document.write( "So t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%288%2F15%29 ALIGN=MIDDLE  ALT=\"1%2F%288%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F8 ALIGN=MIDDLE  ALT=\"15%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F8 ALIGN=MIDDLE  ALT=\"7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "So, our answer is:<br>\r<BR>\n" );
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document.write( "   It would take them 1<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F8 ALIGN=MIDDLE  ALT=\"7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours to rake the lawn and bag the leaves.<br>\r<BR>\n" );
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document.write( "With practice, you will learn to do these steps by writing the problem mathematically, but for now, keep everything clear by writing it down. </SPAN>\n" );
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