document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040981>Question 1040981</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going, in 10 seconds . The speed of the train is - 45 km/ hr, 50 km/hr ,54km/hr,55km/hr<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655908 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=655908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance.<BR>\n" );
document.write( "let r = rate, t = time, d = distance.<BR>\n" );
document.write( "formula becomes: r * t = d<BR>\n" );
document.write( "for the man, the formula becomes 5*t = d.<BR>\n" );
document.write( "this is because the rate of the man is 5 kilometers per hour.<BR>\n" );
document.write( "they both start when the front of the train is at the same location as the man.<BR>\n" );
document.write( "the train has passed the man when the back of the train is at the same location as the man.<BR>\n" );
document.write( "this means that the train must be traveling 125 meters further than the man.<BR>\n" );
document.write( "125 meters is equivalent to .125 kilometers.\r<BR>\n" );
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document.write( "the formula for the man is 5*t = d<BR>\n" );
document.write( "the formula for the train becomes r * t = d + .125\r<BR>\n" );
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document.write( "t = 10 seconds which is equal to 10/3600 hours.<BR>\n" );
document.write( "the formula for the man becomes 5*10/3600 = d.<BR>\n" );
document.write( "you can solve for d to get d = 50/3600 = 5/360 kilometers.<BR>\n" );
document.write( "this means that d = 5/360 kilometers which makes d = .01388888... kilometers.<BR>\n" );
document.write( "the train has to travel .125 kilometers further than that to completely pass the man.<BR>\n" );
document.write( "therefore the formula for the train becomes r * 10/3600 = d + .125.<BR>\n" );
document.write( "this makes r * 10/3600 = .01388888... + .125 = .1388888... kilometers.<BR>\n" );
document.write( "formula for train becomes r * 10/3600 = .1388888... kilometers.<BR>\n" );
document.write( "solve for r to get r = .1388888... * 3600 / 10 = 50 kilometers per hour.<BR>\n" );
document.write( "that's your answer.<BR>\n" );
document.write( "the man travels at 5 kilometers for 10/3600 hours to make a distance of 50/3600 kilometers.<BR>\n" );
document.write( "the train travels at 50 kilometers per hour for 10/3600 hours to make a distance of 500/3600 kilometers.<BR>\n" );
document.write( "the difference of 500/3600 and 50/3600 is equal to 450/3600 which is equal to .125 kilometers.<BR>\n" );
document.write( ".125 kilometers is equal to 125 meters.<BR>\n" );
document.write( "this is the length of the train.<BR>\n" );
document.write( "they started when the front of the train was at the same location as the man.<BR>\n" );
document.write( "they finished when the back of the train was at the same location as the man.\r<BR>\n" );
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document.write( "it was important to get everything in the same measure.<BR>\n" );
document.write( "you could work with kilometers per hour and kilometers, or you could work with meters per second and meters.<BR>\n" );
document.write( "i chose to work with kilometers per hour and kilometers, so i converted everything to kilometers per hour and kilometers.<BR>\n" );
document.write( "125 meters is equal to .125 kilometers.\r<BR>\n" );
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document.write( "what makes this problem difficult is the measurements involved.<BR>\n" );
document.write( "they're just not simple to work with.<BR>\n" );
document.write( "the same problem with simpler measurements would be as follows:<BR>\n" );
document.write( "assume the man travels at 5km per hour for a period of 1 hour.<BR>\n" );
document.write( "assume the train is 2km long.<BR>\n" );
document.write( "they start when the front of the train is at the same location as the man.<BR>\n" );
document.write( "in 1 hour, the front of the train must travel 2km longer than the man.<BR>\n" );
document.write( "the formula for the man is 5*1 = d which makes d = 5 km.<BR>\n" );
document.write( "the front of the train must travel 2km longer in the same time, so the train has to travel 7km in 1 hour.<BR>\n" );
document.write( "the formula for the train becomes r*1 = 7 which makes r = 7 km per hour.<BR>\n" );
document.write( "the man travels 5 km per hour for 1 hour to travel 5 km.<BR>\n" );
document.write( "the front of the train travels 7 km per hour for 1 hour to travel 7 km.<BR>\n" );
document.write( "the front of the train has traveled 2km further than the man, therefore the back of the train is at the same location as the man in 1 hour.<BR>\n" );
document.write( "the following diagram shows this relationship.<BR>\n" );
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