document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120711>Question 120711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> word problem:  Bob climbed down a ladder from his roof, while Rob climbed up another ladder next to him.  Each ladder had 30 rungs.  Their  friend Jill recorded the following info:<BR>\n" );
document.write( "Bob went down 2 rungs every second,  Rob went up 1 rung every second.<BR>\n" );
document.write( "At some point they were at the same hight, what rung were they on.  I know the answer is ten, but I can't come up with the 2 equations that I need to get the answer.  We are working on finding points of intersection.  Can you help me?  Thank! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88512 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=88512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let H represent the height of the individuals in rungs and t represent the time in seconds that <BR>\n" );
document.write( "passes while they climb.<BR>\n" );
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document.write( "Bob starts at rung 30 and goes down at a rate of -2 rungs per second. So the equation for<BR>\n" );
document.write( "Bob's height is:<BR>\n" );
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document.write( "H = -2*t + 30<BR>\n" );
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document.write( "Meanwhile, Rob starts at rung 0 and goes up at a rate of +1 rung per second. So the equation<BR>\n" );
document.write( "for Rob's height is:<BR>\n" );
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document.write( "H = t + 0 = t<BR>\n" );
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document.write( "You are interested in finding the height (in rungs) where the two will be standing on<BR>\n" );
document.write( "the same rung.  Since the two heights are the same, we can set the right sides of our two<BR>\n" );
document.write( "height equations equal. So we can say that:<BR>\n" );
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document.write( "-2*t + 30 = t<BR>\n" );
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document.write( "To solve this equation for t, first get rid of the 30 on the left side by subtracting<BR>\n" );
document.write( "30 from both sides of the equation. This subtraction converts the equation to:<BR>\n" );
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document.write( "-2*t = t - 30<BR>\n" );
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document.write( "Next get rid of the t on the right side by subtracting t from both sides. The equation then<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "-3*t = -30<BR>\n" );
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document.write( "Solve for t by dividing both sides of this equation by -3 to find that:<BR>\n" );
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document.write( "t = -30/-3 = 10 seconds<BR>\n" );
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document.write( "In 10 seconds Rob will have climbed to rung number 10 because he climbs at 1 rung per<BR>\n" );
document.write( "second. And in 10 seconds at a rate of 2 rungs per second Bob will climb down 20 rungs. But <BR>\n" );
document.write( "Bob started on rung 30 so he will be at rung 10 also because 30 - 20 = 10.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better.<BR>\n" );
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document.write( " </SPAN>\n" );
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