document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78502>Question 78502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes me 3 hours to prepare a special dinner in class, when it only took my husband 2 hours. How long will it take for them both to finish the cooking class? Answer should be rounded to the one decimal. Must be shown in a rational equation </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56295 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=56295\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have 1 job ... and that job is cooking the meal.  Since you take 3 hours to do that job,<BR>\n" );
document.write( "your rate of doing it is <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;\" > of the job per hour.  Your husband does the 1 job in<BR>\n" );
document.write( "2 hours, so his rate of doing the job is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job per hour.  When you work together<BR>\n" );
document.write( "your time to complete the 1 job is represented by t.  The equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2At+%2B+%281%2F2%29%2At+=+1+ ALIGN=MIDDLE  ALT=\"%281%2F3%29%2At+%2B+%281%2F2%29%2At+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the 1 represents the entire job.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can add the terms on the left side either by converting the fractions to decimals or<BR>\n" );
document.write( "by putting them over the common denominator of 6.  Let's use the common denominator.<BR>\n" );
document.write( "Recognize that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3+=+2%2F6 ALIGN=MIDDLE  ALT=\"1%2F3+=+2%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2+=+3%2F6 ALIGN=MIDDLE  ALT=\"1%2F2+=+3%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substituting these values makes the <BR>\n" );
document.write( "equation become:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F6%29%2At+%2B+%283%2F6%29%2At+=+1 ALIGN=MIDDLE  ALT=\"%282%2F6%29%2At+%2B+%283%2F6%29%2At+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now add the two terms on the left side to result in:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B3%29%2F6%2At+=+1 ALIGN=MIDDLE  ALT=\"%282%2B3%29%2F6%2At+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and this simplifies to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6%2At+=+1 ALIGN=MIDDLE  ALT=\"5%2F6%2At+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "you can then solve for t by dividing both sides of this equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6 ALIGN=MIDDLE  ALT=\"5%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+1%2F%285%2F6%29 ALIGN=MIDDLE  ALT=\"+t+=+1%2F%285%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then apply the rule that dividing a quantity by a fraction <BR>\n" );
document.write( "is the same as multiplying the quantity by the inverse of the fraction.  This converts<BR>\n" );
document.write( "the equation for t to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1%2A%286%2F5%29+=+6%2F5 ALIGN=MIDDLE  ALT=\"t+=+1%2A%286%2F5%29+=+6%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and when you divide 5 into 6 you get an answer of 1.2 hours. That's the answer ...<BR>\n" );
document.write( "if you and your husband work together you should finish the class in 1.2 hours.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand problems of combined efforts a little better. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );