document.write( "Question 824377: Pipe A takes 16 min to fill a tank. Pipes B and C, whose cross-sectional circumferences are in the ratio 2:3, fill another tank twice as big as the first. If A has a cross-sectional circumference that is one-third of C, how long will it take for B and C to fill the second tank? (Assume the rate at which water flows through a unit cross-sectional area is same for all the three pipes.) \n" ); document.write( "

Algebra.Com's Answer #496521 by Edwin McCravy(20054) $\"\"$ $\"About$

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Pipe A takes 16 min to fill a tank.
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document.write( "So pipe A's filling rate is 1 tank per 16 min or  or \r\n" );
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A has a cross-sectional circumference that is one-third of C

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document.write( "Therefore C's cross-sectional circumference is 3 times A's cross-sectional\r\n" );
document.write( "circumference, and since area varies as the square of the circumference,\r\n" );
document.write( "C's cross-sectional area is 3² or 9 times A's cross-sectional area. \r\n" );
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document.write( "Since

the rate at which water flows through a unit cross-sectional area is same for all the three pipes

 therefore:\r\n" );
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document.write( "Pipe C's filling rate is 9 times A's filling rate or

Pipes B and C's cross-sectional circumferences (are) in the ratio 2:3

Since area varies as the square of the circumference. their cross-sectional\r\n" );
document.write( "areas are in the ratio of 2²:3² or 4:9, and since the rate at which water flows\r\n" );
document.write( "through a unit cross-sectional area is same for all the three pipes, pipe B's\r\n" );
document.write( "filling rate is ths of C's filling rate or  or .

\n" ); document.write( "Pipes B and C fill another tank twice as big as the first.
\n" ); document.write( "how long will it take for B and C to fill the second tank?

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document.write( "B's and C's combined filling rate is \r\n" );
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document.write( "+ = + =  \r\n" );
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document.write( "Since the second tank is twice as big as the first tank (I assume in volume),\r\n" );
document.write( "it is the same as if they filled 2 tanks the size of the tank that A fills.\r\n" );
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document.write( "We will borrow the equation (rate)(time)=(distance covered), from motion\r\n" );
document.write( "problems, by replacing \"distance covered\" by \"tanks filled\". \r\n" );
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document.write( "Let t = the number of minutes it will take B and C to fill 2 tanks:\r\n" );
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document.write( "Then (B and C's combined rate)(time) = (2 tanks) \r\n" );
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document.write( "       t = 2\r\n" );
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document.write( "Multiply both sides by \r\n" );
document.write( "    \r\n" );
document.write( "          t = 2·\r\n" );
document.write( "          t =  = 2.461538462 or about 2.5 minutes.\r\n" );
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document.write( "Edwin

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