document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=350851>Question 350851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two seconds after firing a rifle at a target, the shooter hears the impact of the bullet. Sound travels at 1100 feet per second and the bullet at 1865 feet per second. Determine the distance to the target. \r<BR>\n" );
document.write( "\n" );
document.write( "How do you set up that equation?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #250817 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=250817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sound travels at 1100 feet per second.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "bullet travels at 1865 feet per second.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "person fires bullet and hears the sound of the bullet hitting the target 2 seconds later.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we want to find the distance to the target.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since rate * time = distance, we know that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1865 * x = d\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "where x is the time it takes for the bullet to get to the target and d is the distance to the target.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1100 * y = d where y is the time it takes for the sound of the bullet hitting the target to get back to the shooter and d is the distance from the target to the shooter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the distance to the target and the distance back from the target are the same, then we can set these equations equal to each other to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1865*x = 1100*y = d\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we also know that the total time is equal to 2 seconds.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that x + y must equal 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we can solve for x or y from this equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we'll solve for y.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we get y = (2-x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we take the equation of 1865*x = 1100*y and substitute for y to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1865*x = 1100*(2-x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify this to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1865*x = 2200 - 1100*x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add 1100*x to both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2965*x = 2200\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by 2965 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 2200/2965 = .741989882 seconds\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since x + y = 2, this makes y = 1.258010118\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it takes the bullet .741989882 seconds to reach the target and it takes the sound of the bullet hitting the target 1.258010118 seconds to get back to the shooter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y must equal 2 which we get by adding .741989882 + 1.258010118 = 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the distance to the target and the distance back from the target must be the same.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1865 * .741989882 = 1383.81113 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1100 * 1.258010118 = 1383.81113 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "distances are the same so the numbers must be good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The distance to the target is 1183.81113 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the shooter fires the bullet.<BR>\n" );
document.write( "it takes .741989882 seconds for the bullet to reach the target.<BR>\n" );
document.write( "it takes 1.258010118 seconds for the sound of the bullet hitting the target to get back to the shooter.<BR>\n" );
document.write( "the shooter hears the sound 2 seconds after the shooter fires the bullet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );