document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132273>Question 132273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A truck loaded with vegetables left Station B at 5:00 am and traveled eastward towards town M running at an average speed of 30 kph. At the same time, an express<BR>\n" );
document.write( "bus left Station A, 30 km west of Station B, and traveled eastward towards town M   <BR>\n" );
document.write( "running at an average speed of 50 kph. When will the bus overtake the truck?     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96629 by </B><A HREF=/tutors/aboutme.mpl?userid=nycsharkman><B>nycsharkman(136)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nycsharkman><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=96629\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your question is:\r<BR>\n" );
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document.write( "A truck loaded with vegetables left Station B at 5:00 am and traveled eastward towards town M running at an average speed of 30 kph. At the same time, an express bus left Station A, 30 km west of Station B, and traveled eastward towards town M  running at an average speed of 50 kph. When will the bus overtake the truck?   \r<BR>\n" );
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document.write( "This is a distance word problem.  So, we can use the distance formula D = rt, where d = distance, r = rate or speed and t = time, in hours NOT MINUTES.\r<BR>\n" );
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document.write( "The best thing to do is to set up table. \r<BR>\n" );
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document.write( "Since the truck and bus are going in the same direction, distances are equal, obviously.  \r<BR>\n" );
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document.write( "We know the speed of the truck and bus but we do NOT know the time.  This is what we are searching for.  So, let x represent time of vehicles in hours.\r<BR>\n" );
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document.write( "Truck Data:     \r<BR>\n" );
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document.write( "time = x          \r<BR>\n" );
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document.write( "rate = 30  \r<BR>\n" );
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document.write( "Distance = 30x \r<BR>\n" );
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document.write( "==============\r<BR>\n" );
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document.write( "Bus Data:\r<BR>\n" );
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document.write( "time = x   \r<BR>\n" );
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document.write( "rate = 50\r<BR>\n" );
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document.write( "distance = 50x\r<BR>\n" );
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document.write( "Here is where it gets tricky.\r<BR>\n" );
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document.write( "The question says: \"At the same time, an express bus left Station A, 30 km west of Station B...\"\r<BR>\n" );
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document.write( "That statement is saying that the truck is 30 km ahead of the bus.\r<BR>\n" );
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document.write( "Another way to look at this statement is to say that the bus is 30 km behind the truck also coming from the West heading East.\r<BR>\n" );
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document.write( "50x - 30 = distance of bus MINUS 30 km behind the truck\r<BR>\n" );
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document.write( "30x = truck distance\r<BR>\n" );
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document.write( "Equate and solve for x.\r<BR>\n" );
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document.write( "50x - 30 = 30x\r<BR>\n" );
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document.write( "50x - 30x = 30\r<BR>\n" );
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document.write( "20x = 30\r<BR>\n" );
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document.write( "x = 30/20\r<BR>\n" );
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document.write( "x = 3/2\r<BR>\n" );
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document.write( "What is 3/2 in terms of hours?\r<BR>\n" );
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document.write( "It is 1.5 hours or 1 hour and 30 minutes.  \r<BR>\n" );
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document.write( "When will the bus overtake the truck?  It will overtake the truck in 1 hour and 30 minutes.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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