document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187863>Question 187863</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977223/algebrahomeworkh>algebra structure and methoed</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> solution to work problem\r<BR>\n" );
document.write( "\n" );
document.write( "ramon cna do the weekly billing in 2 hrs luann needs three hours. if roman works for 30 minute and then is joined by luann, how long will it take them to finish\r<BR>\n" );
document.write( "\n" );
document.write( "the tens digit of a two digit number is one more than 3 times the unit digit.<BR>\n" );
document.write( "subtracting 45 from the number reverses it , find the original number\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140904 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=140904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "\n" );
document.write( "If Ramon worked for 30 minutes (1/2 hour) on a job that takes 2 hours, he would have completed 1/4 of the job, leaving 3/4 of the job remaining which would take him 3/2 hours to complete by himself.  If Luann needs 3 hours to do the whole job, then it would take her 3 times 3/4 = 9/4 hours to do the remainder of the job.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If Ramon can do the rest of the job in 3/2 hours, then he can do 2/3 of the job in one hour.  Likewise, Luann can do 4/9 of the job in one hour.  Together, they can do:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{2}{3} + \frac{4}{9} = \frac{6}{9} + \frac{4}{9} = \frac{10}{9}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "of the job in one hour, therefore, it will take them \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{9}{10}\"> of an hour\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to complete the remainder of the job, and \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{9}{10} \times 60 = 54\"> minutes.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "******************************************\r<BR>\n" );
document.write( "\n" );
document.write( "Let <i>x</i> be the tens digit and <i>y</i> be the units digit.  We are given that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  x = 3y + 1\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, the number must be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  10x + y\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And the number reversed must be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  10y + x\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And we are given that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  10x + y - 45 = 10y + x\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  9x - 9y = 45\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  x - y = 5\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substituting:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  (3y + 1) - y = 5\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  3y + 1 - y = 5\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  2y = 4\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  y = 2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the units digit is 2 and the tens digit is 3(2) + 1 = 7.  And the number is then 72.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  72 - 45 = 27\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer checks.<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );