document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=828314>Question 828314</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes Brian 15 hours longer to build a model car than it takes John. If they work together, they can build the model car in 4 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Brian to build the car on his own.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499232 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=499232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, we want to determine the rate at which both John and Brian work.\r<BR>\n" );
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document.write( "Since we don't know how long it takes John to build the car, we will let x denote this time. \r<BR>\n" );
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document.write( "If it takes John x hours to build the car, then we know that it takes Brian (x+15) hours to build the car because that's what the problem states.\r<BR>\n" );
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document.write( "If we can set up an equation that determines x, then all we need to do is add 15 hours to it and we have Brian's time.\r<BR>\n" );
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document.write( "Now, we can determine the rate at which each boy works.  We can clearly see that John works at the rate of 1/x of the model car per hour and Brian works at the rate of 1/(x+15) of the model car per hour.\r<BR>\n" );
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document.write( "We are told that if they work together, they can build the model car in 4 hours which means that, together, they work at the rate of 1/4 of the model car per hour.\r<BR>\n" );
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document.write( "We also know that, together, they work at the rate of 1/x + 1/(x+15) of the model car per hour.\r<BR>\n" );
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document.write( "Thus, our equation to solve is:<BR>\n" );
document.write( "1/x + 1/(x+15)=1/4 \r<BR>\n" );
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document.write( "When we solve this equation for x and add 15 hours to it, we will have solved the problem:)\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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