document.write( "Question 1106369: A piece of land is 20 miles in circumference. Three persons, A, B, and C, start from the same place and travel the same way. A travels 3 mph, B 7 mph, and C 11 mph. In what time will they be together again?\r
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Algebra.Com's Answer #721353 by ikleyn(52786) $\"\"$ $\"About$

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document.write( "In 5 hours person A will cover 5*3 = 15 miles.\r\n" );
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document.write( "           person B will cover 5*7 = 35 miles,  which is one entire circumference of 20 miles plus the same 15 miles: 35 = 20 + 15.\r\n" );
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document.write( "           person C will cover 5*11 = 55 miles, which is TWO TIMES entire  circumference of 20 miles plus the same 15 miles: 55 = 2*20 + 15.\r\n" );
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document.write( "So, in 5 hours all three of them will be at the same point on the circumference.\r\n" );
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document.write( "To that time person A will be on the way making his first lap;\r\n" );
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document.write( "             person B will complete his first lap and will be on the way making his 2-nd lap;\r\n" );
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document.write( "         and person C will complete his TWO laps and will be on the way making his 3-rd lap.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is informal solution.\r
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\n" ); document.write( "\n" ); document.write( "The formal solution is based on the following fact:\r
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document.write( "    For two bodies that started simultaneously from one point and move uniformly along the circle (along the closed path) of \r\n" );
document.write( "    the circumference S in the same direction with different speeds/rates  and ,  > , the time from the start till the moment\r\n" );
document.write( "    when the faster body will catch the slower body is this condition\r\n" );
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document.write( "         = S:     the difference between the covered distanses is exactly equal to the circumference.\r\n" );
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document.write( "    It is also the condition for the time duration between any two consecutive catching moments.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Problems on bodies moving on a circle \r
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