document.write( "Question 1055382: A person sets out from Boston and walks toward Portland at the rate of3.0km/h . Three hours afterward, a second person sets out from the same place and walks in the same direction at the rate of 4.0km/h . How far from Boston will the second person overtake the first? \n" ); document.write( "

Algebra.Com's Answer #670613 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "A person sets out from Boston and walks toward Portland at the rate of 3.0 km/h. Three hours afterward, a second person sets out
\n" ); document.write( "from the same place and walks in the same direction at the rate of 4.0 km/h.
\n" ); document.write( "How far from Boston will the second person overtake the first?
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\n" ); document.write( "\n" ); document.write( "Solution 1 (for those who is novice in Travel and Distance problems)\r
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document.write( "Let t be the time (in hours) counted from the moment the second person started from Boston to the the overtaking moment.\r\n" );
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document.write( "Then the distance covered by the second person is his rate multiplied by time:\r\n" );
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document.write( "d = 4*t.        (1)\r\n" );
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document.write( "For the first person his time from his start to the overtaking moment is (t+3) hours.\r\n" );
document.write( "Therefore, the distance covered by the first person during this time is\r\n" );
document.write( "d = 3*(t+3).    (2)\r\n" );
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document.write( "The distance (1) and (2) is actually the same (!).  It is the key moment in the solution (!!)\r\n" );
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document.write( "Therefore, you have an equation\r\n" );
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document.write( "4t = 3(t+3).\r\n" );
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document.write( "Simplify and solve it for t:\r\n" );
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document.write( "4t = 3t + 9,  or\r\n" );
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document.write( "4t - 3t = 9,\r\n" );
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document.write( "t = 9.\r\n" );
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document.write( "So, you found that the second person will overtake the first one after 9 hours after the second person start.\r\n" );
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document.write( "During this time, the second person vill cover 9*6 = 36 kilometers.\r\n" );
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document.write( "Thus the overtaking point is 36 kilometers apart Boston.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution 2 (for \"physicists\", who love short solutions)\r
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document.write( "When the second started, the first was just in 3*3 = 9 km from the starting point.\r\n" );
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document.write( "The distance between them decrease 1 kilometer per each hour: 1 = 4 - 3 (!).\r\n" );
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document.write( "So, it will take 9 hours for the second to catch the first.\r\n" );
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document.write( "In 9 hours, the second will cover 4*9 = kilometers (!).\r\n" );
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document.write( "The same answer (!!).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution 3 (for \"the true physicists\", who love short formulas)\r
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document.write( "The \"true\" physicist, or, in general, an advanced person writes momentarily\r\n" );
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document.write( "     t =  = 9 hours for the second to catch the first.\r\n" );
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document.write( "     d = 9*4 = 36 kilometers (the distance)\r\n" );
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document.write( "and everything is clear to him without any explanations.\r\n" );
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document.write( "It is the level you should to strive for.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "For Travel and Distance problems see an introductory lesson \r
\n" ); document.write( "\n" ); document.write( " - Travel and Distance problems \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this textbook under the section \"Word problems\", the topic \"Travel and Distance problems\".\r
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