document.write( "Question 1145856: I would appreciate if someone could help me on this problem-please if you could show the work so I can understand it. Thanks\r
\n" ); document.write( "\n" ); document.write( "A pirate sails in a circular route around point A,
\n" ); document.write( "as shown to the right, with a circumference of
\n" ); document.write( "32 km, and a merchant ship sails in a circular
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\n" ); document.write( "If they both start where the routes meet, and the pirate
\n" ); document.write( "sails 12 km per day and the merchant sails at 8 km per
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Algebra.Com's Answer #767137 by ikleyn(52858) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            First of all, nothing is shown to the right, although the post promises it.\r
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\n" ); document.write( "\n" ); document.write( "            I understand your difficulties. In such case, you MUST provide an adequate wording description.\r
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\n" ); document.write( "\n" ); document.write( "            I strongly (strictly) suspect that these circles touch each other, having one (and only one) common point.\r
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document.write( "            (Simply because I do not see any other alternative possibility).\r\n" );
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\n" ); document.write( "\n" ); document.write( " If so (I am 129% confident it is so), then the solution can be easily done as follows.\r
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document.write( "The pirate' ship makes   =  of his circle per day.\r\n" );
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document.write( "It needs 8 days to make 3 circles, and it makes integer number of circles every 8 days  (as a check, 8*12 = 96 = 32*3 miles.)\r\n" );
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document.write( "The merchant ship makes   =  of his circle per day.\r\n" );
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document.write( "It needs 6 days to make 1 circle, and it makes integer number of circles every 6 days  (as a check, 6*8 = 48 = 48 miles.)\r\n" );
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document.write( "The two ships can meet each other at the touching point ONLY, and\r\n" );
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document.write( "for it, each ship should make integer number of their corresponding circles.\r\n" );
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document.write( "Therefore, we should find the Least Common Multiple of the integer numbers 8 and 6.\r\n" );
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document.write( "This LCM = LCM(8,6) = 24.\r\n" );
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document.write( "ANSWER.  In 24 days.\r\n" );
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document.write( "CHECK.  In 24 days, the pitate' ship will make  = 9 full circles;\r\n" );
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document.write( "        in 24 days, the merchant ship will make   = 4 full circles.\r\n" );
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document.write( "        Thus after 24 days each of them will complete the integer number of their corresponding circles \r\n" );
document.write( "        and, hence, they will meet each other again for the first time.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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