document.write( "Question 1166905: A kayaker was paddling due East at 3mph and an orca was swimming due North at 10mph. If they started 1 mile apart, how long did it take for the orca to swim underneath the kayaker? Model this problem with an algebraic equation. Show work! \n" ); document.write( "

Algebra.Com's Answer #852247 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A kayaker was paddling due East at 3mph and an orca was swimming due North at 10mph.
\n" ); document.write( "If they started 1 mile apart, how long did it take for the orca to swim underneath the kayaker?
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document.write( "Let 't' be the time under the problem's question.\r\n" );
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document.write( "To get the meeting point, the kayaker paddled 3t miles to the east.\r\n" );
document.write( "while the orca swam 10t miles to the North.\r\n" );
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document.write( "According to the problem, these distances, 3t miles and 10t miles, \r\n" );
document.write( "are the legs of a right-angled triangle, whose hypotenuse is 1 mile.\r\n" );
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document.write( "So, we write the Pythagorean equation\r\n" );
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document.write( "     +  = 1,\r\n" );
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document.write( "     +  = 1,\r\n" );
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document.write( "     = 1,\r\n" );
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document.write( "     = ,\r\n" );
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document.write( "    t =  = 0.095782629 of an hour, or 0.095782629*60 = 5.746957711 minutes.\r\n" );
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document.write( "ANSWER.  The time is about 5.747 minutes.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "This problem is nice and interesting.
\n" ); document.write( "You can solve it considering the events in reverse time, assuming that the kayaker and the orca
\n" ); document.write( "move in perpendicular directions back from the meeting point to their starting positions.\r
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\n" ); document.write( "\n" ); document.write( "Then after t hours the distance between them will be 1 mile,
\n" ); document.write( "and from this condition it is easy to find time 't'.\r
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\n" ); document.write( "\n" ); document.write( "Thus we have simple, elegant and unexpectedly short solution.\r
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