document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087986>Question 1087986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jessie and Mark are planning to paint a house together. Jessie thinks that if he works alone, it would take him 5 hours more than the time Mark takes to paint the entire house. Working together, they can complete the job in 6 hours.\r<BR>\n" );
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document.write( "QUESTION: How will you solve the equation formulated? What mathematics concepts and principles are you going to use? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702252 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=702252\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let m = the amount of time required by Mark to paint the entire house alone <BR>\n" );
document.write( "Thus, their rates of painting will be 1/m and 1/(m+5) houses per hour<BR>\n" );
document.write( "Working together their combined rate is:<BR>\n" );
document.write( "1/m + 1/(m+5) = 1/6 [houses per hour]<BR>\n" );
document.write( "The above expression tells us how much of the house they complete every hour working together<BR>\n" );
document.write( "Solve for m:<BR>\n" );
document.write( "m^2 + 5m = 12m + 30<BR>\n" );
document.write( "m^2 - 7m - 30 = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "(m-10)(m+3) = 0<BR>\n" );
document.write( "Take the positive solution, m = 10 [hours]<BR>\n" );
document.write( "So Mark's rate of painting is 1/10 houses per hour and Jessie's rate is 1/15 houses per hour.<BR>\n" );
document.write( "If it's confusing, take a simple example.  Suppose someone can perform a task, say clean their room, in 2 hours.  <BR>\n" );
document.write( "That means they can clean 1/2 of their room every hour [this is their rate of working]<BR>\n" );
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