document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=838771>Question 838771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Car A travels 120 miles in the same time that car B travels 150 miles. If car B travels 10 mph faster than car A, how fast is each car travelling? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505327 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=505327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general equation to use is:<BR>\n" );
document.write( "RT = D<BR>\n" );
document.write( "this equations means:<BR>\n" );
document.write( "rate * time = distance.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "car A travels 120 miles in the same time that car B travels 150 miles.<BR>\n" );
document.write( "If car B travels 10 mph faster than car A, how fast is each car travelling.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since they both travel for the same amount of time, we'll let T represent the amount of time it takes in hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If we allow the rate of car A to be equal to R, then the rate of car B will have to be R + 10 because car B travels 10 miles per hour faster than car A.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation for car A becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "R * T = 120\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation for car B becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(R + 10) * T = 150\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "these are 2 equations that need to be solved simultaneously in order to find the same answer that is applicable to both.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "those equations are:<BR>\n" );
document.write( "R * T = 120<BR>\n" );
document.write( "(R + 10) * T = 150\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we'll solve by substitution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the equation of R * T = 120, solve for T to get:<BR>\n" );
document.write( "T = 120 / R\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the equation of (R + 10) * T = 150, replace T with 120 / R to get:<BR>\n" );
document.write( "(R + 10) * 120 / R = 150\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for R in this equation as follows:<BR>\n" );
document.write( "start with:<BR>\n" );
document.write( "(R + 10) * 120 / R = 150<BR>\n" );
document.write( "multiply both sides of this equation by R to get:<BR>\n" );
document.write( "(R + 10) * 120 = 150 * R<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "120 * R + 1200 = 150 * R<BR>\n" );
document.write( "subtract 120 * R from both sides of this equation to get:<BR>\n" );
document.write( "1200 = 150 * R - 120 * R<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "1200 = 30 * R<BR>\n" );
document.write( "divide both sides of this equation by 30 to get:<BR>\n" );
document.write( "40 = R\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since R = 40, then R + 10 must be equal to 50.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "car A is traveling at 40 miles per hour.<BR>\n" );
document.write( "car B is traveling at 50 miles per hour.<BR>\n" );
document.write( "those are your answers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we'll use those values for R in the original equations to see if they make sense.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the first equation, we have:<BR>\n" );
document.write( "R * T = 120<BR>\n" );
document.write( "since R = 40, this equation becomes:<BR>\n" );
document.write( "40 * T = 120<BR>\n" );
document.write( "divide both sides of this equation by 40 and you get:<BR>\n" );
document.write( "T = 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the second equation, we have:<BR>\n" );
document.write( "(R + 10) * T = 150<BR>\n" );
document.write( "since R = 40, thyis equation becomes:<BR>\n" );
document.write( "(40 + 10) * T = 150<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "50 * T = 150<BR>\n" );
document.write( "divide both sides of this equation by 50 to get:<BR>\n" );
document.write( "T = 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "both cars travel for the same time.<BR>\n" );
document.write( "car B is traveling 10 miles per hour faster than car A.<BR>\n" );
document.write( "everything checks out, so the solution is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "car A is traveling at 40 miles per hour.<BR>\n" );
document.write( "car B is traveling at 50 miles per hour.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "extra information:<BR>\n" );
document.write( "they are both traveling for 3 hours each.\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( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );