document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165401>Question 1165401</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An auto A is moving at 30 fps and accelerating at 5 fps^2 to overtake an auto B<BR>\n" );
document.write( "which is 384 ft ahead. Auto B is moving at 60 fps and decelerating at 3 fps^2<BR>\n" );
document.write( "(a) How soon will A pass B? <BR>\n" );
document.write( "(b) What is the total distance traveled by car A? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789893 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=789893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe the distance formula for an accelerating car is y = ax + (b/2)x^2 and the distance formula for a decelerating car is y = ax - (b/2)x^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x is the number of seconds.<BR>\n" );
document.write( "y is the distance traveled in x seconds.<BR>\n" );
document.write( "a is the constant velocity<BR>\n" );
document.write( "b is the constant constant acceleration.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "applying this to your situation gets you.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 30 * x + 5/2 * x^2 for the accelerating car.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 60 * x - 3/2 * x^2 for the decelerating car.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both cars will have traveled the same distance when 30 * x + 5/2 * x^2 = 60 * x - 3/2 * x^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = 7.5 seconds.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both cars will have traveled the same distance in 7.5 seconds, after w hich the accelerating car will have passed the decelerating car.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "at this point in time, the distanced traveled by each car will be 365.625 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equations for each car can be graphed.<BR>\n" );
document.write( "the intersection of the lines on the graph is when both cars will have traveled the same distance.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation for the accelerating car is y = 30x + 5/2 * x^2.<BR>\n" );
document.write( "the equation for the decelerating cvar is y = 60x - 3/2 * x^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph confirms the solution expressed above (365.625 feet in 7.5 seconds for both cars).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/092101.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i also used a calculator to confirm the formulas were correctly applied.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the accelerating car .....\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/092102.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the decelerating car .....\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/092103.jpg\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both the graph and the calculator confirm the calculations are correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this assumes, of course, that i'm using the right formula.<BR>\n" );
document.write( "i'm reasonably confident that i am.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );