document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113213>Question 113213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At 9:00am a truck leaves the truck yard and travels west at a rate of 45mi/hr. Two hours later, a second truck leaves along the same route, travelling at 75 mi/hr. When will the second truck catch up to the first?<BR>\n" );
document.write( "What I have so far is this 45(x)=75(x+2). Would this be correct so far?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you for your help,<BR>\n" );
document.write( "Barb Neely  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82398 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82398\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Almost correct ... you are using the distance formula which says that the distance the first<BR>\n" );
document.write( "truck travels is 45 mph times x hours. The second truck travels at a rate of 75 mph, but<BR>\n" );
document.write( "it travels 2 hours less than x.  So the time this second truck travels is x - 2, not x + 2.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "When the two trucks are finally the side-by-side, they are equal distance from the starting point<BR>\n" );
document.write( "so their two distances are equal. In equation form this is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "45x = 75(x-2)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Multiply out the right side and this equation becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "45x = 75x - 150<BR>\n" );
document.write( ".<BR>\n" );
document.write( "get rid of the -150 on the right side by adding +150 to both sides and the equation becomes<BR>\n" );
document.write( ".<BR>\n" );
document.write( "45x + 150 = 75x<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next get rid of the +45x on the left side by subtracting 45x from both sides and you have:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "+150 = 30x<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Finally solve for x by dividing both sides by 30 to get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x = 150/30 = 5 hours<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Adding 5 hours to 9:00 a.m. means that at 2:00 p.m. the second truck catches up to the first truck.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "5 hours after it pulls out, the first truck has gone 45*5 = 225 miles. The second truck<BR>\n" );
document.write( "leaves 2 hours later (at 11:00 a.m.) and in the 3 hours until 2:00 p.m. It goes 75*3 = 225 miles<BR>\n" );
document.write( "from the starting point ... so the two trucks are equally as far from the starting point.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Another way you can look at this problem is to say that in the 2 hours the first truck travels<BR>\n" );
document.write( "by itself it goes 90 miles. So it has a 90 mile head start. The second truck sets out at<BR>\n" );
document.write( "11:00 a.m. and it is traveling 30 mph faster than the first truck. Therefore, each hour<BR>\n" );
document.write( "it is on the road it will make up 30 miles. To make up the 90 mile difference, therefore,<BR>\n" );
document.write( "it will be 3 hours after the second truck departs that it will catch up to the first truck.<BR>\n" );
document.write( "So the time it catches up is 3 hours after 11:00 a.m. which again is 2:00 p.m.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the problem a little better.<BR>\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );