document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156500>Question 1156500</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A tour bus normally leaves for its destination at 5:00 p.m. for a 378 mile trip. This week however, the bus leaves at 6:00 p.m. To arrive on time, the driver drives 9 miles per hour faster than usual. What is the bus` usual speed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779228 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=779228\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You should know how to set up and solve the problem using formal algebra, as shown by the other tutors.  Note, however, that with that path you end up having to solve a quadratic equation by factoring by finding two numbers whose difference is 9 and whose product is 3402.<br><BR>\n" );
document.write( "So if a formal algebraic solution is not required, you can find the answer faster by finding two integer factorizations of 378 that satisfy the conditions of the problem.<br><BR>\n" );
document.write( "378 = 2*3*3*3*7<br><BR>\n" );
document.write( "Playing with that prime factorization to find ways to get 378 as a product of two integers finds what we need: 54 times 7 and 63 times 6.<br><BR>\n" );
document.write( "That gives us 378 miles = 7 hours at 54mph or 6 hours at 63mph.<br><BR>\n" );
document.write( "So the regular speed of the bus is 54mph.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );