document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200144>Question 1200144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Joe and Frank want to meet each other half way between their cities. The distance between their towns is 36 miles. Both travel at6 miles per hour. Joe takes a carrier pigeon and sets it off toward Frank. The pigeon travels at 18 miles an hour. When it reaches Frank it turns around immediately and returns to Joe. What is the distance the pigeon covers when the two friends meet. The pigeon does not take a rest.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834185 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=834185\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Draw a number line. Plot A and B on it<BR>\n" );
document.write( "A = 0<BR>\n" );
document.write( "B = 36<BR>\n" );
document.write( "Then plot C at the midpoint 18\r<BR>\n" );
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document.write( "I'll have Joe start at point A, and Frank start at point B. <BR>\n" );
document.write( "Both men are traveling to meet at point C.\r<BR>\n" );
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document.write( "The pigeon starts at point A.<BR>\n" );
document.write( "Its speed is 18 mph, so it travels a distance of 18t where t is the elapsed time in hours.<BR>\n" );
document.write( "distance = rate*time\r<BR>\n" );
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document.write( "Meanwhile, Frank travels a distance of 6t miles.<BR>\n" );
document.write( "Add the expressions 18t and 6t. Then set the sum equal to the total distance 36 to solve for t.<BR>\n" );
document.write( "This is because the pigeon meets Frank, so the two must travel a total distance of 36 miles.\r<BR>\n" );
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document.write( "18t+6t = 36<BR>\n" );
document.write( "24t = 36<BR>\n" );
document.write( "t = 36/24<BR>\n" );
document.write( "t = 1.5\r<BR>\n" );
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document.write( "The pigeon meets Frank at exactly the 1.5 hour marker.\r<BR>\n" );
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document.write( "The pigeon has traveled 18t = 18*1.5 = 27 miles in this time frame.<BR>\n" );
document.write( "Joe has traveled 6t = 6*1.5 = 9 miles in this time frame.<BR>\n" );
document.write( "This means the pigeon would travel 27-9 = 18 additional more miles to get back to Joe if Joe stopped moving.\r<BR>\n" );
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document.write( "However, Joe keeps moving.<BR>\n" );
document.write( "His location on the number line is still 6t.\r<BR>\n" );
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document.write( "When flying back to Joe, the pigeon's location on the number line is 27-18(t-1.5)<BR>\n" );
document.write( "The 27 refers to how far the pigeon has flown to the right. Then we subtract off 18(t-1.5) to go to the left.<BR>\n" );
document.write( "The t-1.5 offsets the time value (to account for the fact the bird has flown 1.5 hours already)\r<BR>\n" );
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document.write( "To summarize:<BR>\n" );
document.write( "Joe's location is 6t<BR>\n" );
document.write( "The pigeon's location after 1.5 hours is 27-18(t-1.5)\r<BR>\n" );
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document.write( "Set them equal to each other to determine the time value when the pigeon meets Joe again.<BR>\n" );
document.write( "27-18(t-1.5) = 6t<BR>\n" );
document.write( "27-18t+27 = 6t<BR>\n" );
document.write( "54-18t = 6t<BR>\n" );
document.write( "54 = 6t+18t<BR>\n" );
document.write( "54 = 24t<BR>\n" );
document.write( "t = 54/24<BR>\n" );
document.write( "t = 9/4<BR>\n" );
document.write( "t = 2.25\r<BR>\n" );
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document.write( "The pigeon meets Joe again at exactly the 2.25 hour marker.<BR>\n" );
document.write( "The pigeon has flown a total distance of 18t = 18*2.25 = <font color=red>40.5 miles</font>.\r<BR>\n" );
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document.write( "Check out this interactive GeoGebra applet.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.geogebra.org/m/uubrrczn\">https://www.geogebra.org/m/uubrrczn</a><BR>\n" );
document.write( "If the page is blank, then hover your mouse over it to have the curved arrow show up. <BR>\n" );
document.write( "Then click on the arrow. The page should refresh to show the interactive diagram.\r<BR>\n" );
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document.write( "Move the slider t so that you can see Joe, Frank, and the pigeon move. <BR>\n" );
document.write( "P1 represents the pigeon's location in the interval 0 < t < 1.5<BR>\n" );
document.write( "P2 represents the pigeon's location in the interval 1.5 < t < 3<BR>\n" );
document.write( "The points J and P2 line up perfectly when t = 2.25\r<BR>\n" );
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document.write( "Answer: <font color=red>40.5 miles</font>\r<BR>\n" );
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document.write( "Edit: I'm realizing I misread the instructions a bit. The answer of 40.5 miles would be correct if it asked \"What is the distance the pigeon covers when the pigeon gets back to Joe\". <BR>\n" );
document.write( "Refer to the solution the tutor @ikleyn has written for the correct answer of 54 miles. <BR>\n" );
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