document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=954712>Question 954712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How long is the train?\r<BR>\n" );
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document.write( "A train moving 45 kilometres per hour meets and is passed by a train moving 36 kilometres per hour. A passenger in the first train sees the second train take 6 seconds to pass him. How long is the second train? </SPAN>\n" );
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document.write( "A train moving 45 kilometres per hour meets and is passed by a train moving 36 kilometres per hour. A passenger in the first train sees the second train take 6 seconds to pass him. How long is the second train?\r<BR>\n" );
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document.write( "the trains are traveling in opposite directions, so their rates relative to each other are additive.\r<BR>\n" );
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document.write( "the net rate of travel is 45 + 36 = 81 kmph.\r<BR>\n" );
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document.write( "if the second train was standing still, it would seem like the first train was passing it at 81 kmph.\r<BR>\n" );
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document.write( "if the first train was standing still, it would seem like the second train was passing it at 81 kmph.\r<BR>\n" );
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document.write( "the passenger in the first train sees the second train for 6 seconds.\r<BR>\n" );
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document.write( "81 kmph is equivalent to 81 / 3600 = .0225 kmps (kilometers per second)\r<BR>\n" );
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document.write( "multiply that by 6 seconds and you get a distance of 6 * .0225 = .135 km.\r<BR>\n" );
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document.write( "that's because rate * time = distance and so .0225 kmps * 6 seconds = .135 km.\r<BR>\n" );
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document.write( "the train is .135 km in length.\r<BR>\n" );
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document.write( "this is because the passenger in the first train sees the front of the second train and 6 seconds later sees the back of the second train.\r<BR>\n" );
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document.write( "there are 3280.84 feet per kilometer, so the train is .135 * 3280.84 = 442.9134 feet in length.\r<BR>\n" );
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document.write( "you can also think of this another way.\r<BR>\n" );
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document.write( "the trains are traveling at 45 kmph and 36 kmph in opposite directions.\r<BR>\n" );
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document.write( "45 kmph is equivalent to 45 / 3600 = .0125 kmps (kilometers per second).\r<BR>\n" );
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document.write( "36 kmph is equivalent to 36 / 3600 = .01 kmps.\r<BR>\n" );
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document.write( "the passenger sees the front of the second train.\r<BR>\n" );
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document.write( "6 seconds the passenger sees the back of the second train.\r<BR>\n" );
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document.write( "in those 6 seconds.\r<BR>\n" );
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document.write( "the first train has traveled 6 * .01 = .06 km in one direction.\r<BR>\n" );
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document.write( "the second train has traveled 6 * .0125 = .075km in the other direction.\r<BR>\n" );
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document.write( "the distance between the front and the back of the second train has to be .06 plus .075 = .135 km.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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