document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=342339>Question 342339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ava rode her bike from her house to her friends house averaging 16 km per hour. It turned dark so her friend drove her home at a rate of 80 km per hour. If Ava's  total traveling time was 3 hours, how far away did her friend live?\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #245021 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=245021\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula we will use is R * T = D where R = rate of speed in km/hr, T = time in hr, and D = distance in km.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We let T = total time it took to get there and back.<BR>\n" );
document.write( "We let D = total distance from there and back.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Going to her friend's house, we let x = the amount of time it took, and we let D/2 = the distance she traveled, and we let 16 = the rate of her speed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The formula for her going is 16 * x = D/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Coming back from her friend's house, we let T-x = the amount of time it took, and we let D/2 = the distance she traveled, and we let 80 = the rate of her speed in her friend's car.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The formula for her coming back is 80 * (T-x) = D/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Both of these formulas are equal to D/2, so they are both equal to each other.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "16 * x = 80 * (T - x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We expand these formulas by removing parentheses to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "16 * x = 80 * T - 80*x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We add 80*x to both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "16*x + 80*x = 80*T\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We combine like terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "96*x = 80*T\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We know that T = 3 hours because that's what we were given.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Our formula becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "96*x = 80 * 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This becomes 96 * x = 240\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We divide both sides of this equation by 96 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 240/96 which makes x = 2.5 hrs.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since T is equal to x + (T-x), then (T-x) has to be .5 hrs.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now that we know x and T-x, we can solve for D/2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In the formula where Ava goes to her friend's house, we get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "16 * x = D/2 becoming 16 * 2.5 = D/2 which makes D/2 equal to 40 km.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In the formula where Ava comes back from her friend's house, we get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "80 * (T-x) = D/2 becoming 80 * .5 = D/2 which makes D/2 equal to 40 km.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Both formulas point to the same distance as they should.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The distance from Ava'a house to her friend's house is equal to 40 km.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "40 km = D/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "D is the distance there and back.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "D is therefore equal to 80 km.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "But you didn't want D.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You wanted D/2 which is the distance from Ava's hour to her friend's house.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your answer is therefore equal to 40 km.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );