document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80830>Question 80830</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two vagabonds who are 200 miles apart travel towards each other.  If they start at 2 p.m. and meet at 6 p.m., and one vagabond is traveling 10 miles per hour faster than the other, what are the speeds of both vagabonds?\r<BR>\n" );
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document.write( "I tried using rate x time = distance like our teacher said, and this is what i got::<BR>\n" );
document.write( "((Vagabond A, Vagabond B))\r<BR>\n" );
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document.write( "..........(r)........(t)..=..d<BR>\n" );
document.write( "A........x         <BR>\n" );
document.write( "B........x+10<BR>\n" );
document.write( "total................4h.....200mi\r<BR>\n" );
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document.write( "Then i divided 200 by 4 and got 50, so I got 50 mph and 60 mph... am I right?\r<BR>\n" );
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document.write( "Thank You!\r<BR>\n" );
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document.write( "Jamie </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58024 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=58024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's check your answer.  One vagabond is going at a rate of 50 miles per hour. The time<BR>\n" );
document.write( "at this rate is 4 hours (2 pm to 6 pm). In that 4 hour period at 50 miles per hour, that<BR>\n" );
document.write( "vagabond travels the full 200 miles by itself. If that doesn't seem right, it means that<BR>\n" );
document.write( "your answer is incorrect because the second vagabond wasn't even taken into consideration.<BR>\n" );
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document.write( "Here's the way to do the problem.<BR>\n" );
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document.write( "Use the distance formula for the vagabond that travels at the unknown rate R. When you do you<BR>\n" );
document.write( "get that the distance (D1) for the first vagabond is:<BR>\n" );
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document.write( "D1 = R*T<BR>\n" );
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document.write( "At this point we know that T is 4 hours. So we can substitute 4 for T and the equation<BR>\n" );
document.write( "then becomes:<BR>\n" );
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document.write( "D1 = R*4 = 4R<BR>\n" );
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document.write( "Now let's do the same thing for the second vagabond. It has a rate equal to the rate of<BR>\n" );
document.write( "the first vagabond plus 10 miles per hour, so its rate is R+10. It also travels for 4 hours.<BR>\n" );
document.write( "If the distance traveled by this second vagabond is D2 then its distance equation is:<BR>\n" );
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document.write( "D2 = (R+10)*4<BR>\n" );
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document.write( "Multiply out the right side and you get:<BR>\n" );
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document.write( "D2 = 4R + 40<BR>\n" );
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document.write( "Now recognize that when the two vagabonds meet, the total distance (D1 + D2) that they<BR>\n" );
document.write( "travel is 200 miles. So lets add our two distance equations:<BR>\n" );
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document.write( "D1 = 4R<BR>\n" );
document.write( "D2 = 4R + 40<BR>\n" );
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document.write( "When you add these vertically you get:<BR>\n" );
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document.write( "D1 + D2 = 8R + 40<BR>\n" );
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document.write( "But we already noted that D1 + D2 is 200 miles.  So we can substitute 200 for D1 + D2 and<BR>\n" );
document.write( "we get:<BR>\n" );
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document.write( "200 = 8R + 40<BR>\n" );
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document.write( "Get rid of the 40 on the right side by subtracting 40 from both sides.  When you do that the<BR>\n" );
document.write( "equation becomes:<BR>\n" );
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document.write( "160 = 8R<BR>\n" );
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document.write( "Finally, solve for R by dividing both sides by 8 and you get:<BR>\n" );
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document.write( "R = 160/8 = 20 miles per hour<BR>\n" );
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document.write( "So the rate of the first vagabond is 20 miles per hour and the rate of the second vagabond<BR>\n" );
document.write( "is 10 miles per hour faster or 30 miles per hour.<BR>\n" );
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document.write( "Let's check these answers.<BR>\n" );
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document.write( "At 20 miles per hour, in 4 hours the first vagabond goes 80 miles toward the second vagabond.<BR>\n" );
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document.write( "Meanwhile at 30 miles per hour, in 4 hours the second vagabond goes 120 miles toward the<BR>\n" );
document.write( "first vagabond.  <BR>\n" );
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document.write( "This combination means that in the 4 hours the two together cover 80 + 120 miles and when <BR>\n" );
document.write( "that is done they meet having covered the 200 miles between them when they started out.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how your teacher said you could use<BR>\n" );
document.write( "the distance formula to solve it. </SPAN>\n" );
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