document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005061>Question 1005061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A city bus finishes its 96 mile route in the same amount of time that a rural bus finishes its 144 mile route. The city bus averages 18 mph slower than the rural bus. How long does it take each bus to finish its route?<BR>\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 #621395 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=621395\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "city bus distance = 96 miles.<BR>\n" );
document.write( "rural bus distance = 144 miles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "city bus rate = 18 mph less than the rural bus rate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assume the rural bus rate is x miles per hour.<BR>\n" );
document.write( "the city bus rate is therefore x - 18\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the city bus:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "rate * time = distance becomes (x-18) * time = 96\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the rural bus:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "rate * time = distance becomes x * time = 144\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "time is the same for both.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we'll solve each equation for time to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "time = 96 / (x-18) for the city bus.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "time = 144 / x for the rural bus.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we replace time in the second equation with the equivalent value for time in the first equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "96 / (x-18) = 144 / x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we  multiply both sides of the equation by (x-18) * x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x * (x-18) * 96 / (x-18) = x * (x-18) * 144 / x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x * 96 = (x-18) * 144\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we simplify further to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x * 96 = 144 * x - 18 * 144\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we simplify further to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "96x = 144x - 2592\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we subtract 96x from both sides of this equation and add 2592 to both sides of this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2592 = 144x - 96x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2592 = 48x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we divide both sides of this equation by 48 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2592 / 48 = x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we solve for x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 54\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the rate of the rural bus.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the rate of the city bus is 18 mph less than that.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the rate of the city bus is 54 - 18 = 36 mph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the rural bus travels at 54 mph.<BR>\n" );
document.write( "the city bus travels at 36 mph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if we did this correctly, time should be the same for both buses.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the city bus, the formula is 36 * time = 96 miles<BR>\n" );
document.write( "solve for time to get time = 96 / 36 = 8/3 hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the rural bus, the formula is 54 * time = 144 miles<BR>\n" );
document.write( "solve for time to get time = 144 / 54 = 8/3 hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "time is the same for both so we're done.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they asked for how long each bus took to finish its route.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the solution is that each bus took 8/3 hours to finish its route.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is equivalent to 2 and 2/3 hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "as a bonus, we also figured out how fast each bus was traveling.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the city bus was traveling at 36 miles per hour.<BR>\n" );
document.write( "the rural bus was traveling at 54 miles per hour.\r<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" );