In what time would a cistern be filled by thr | vedclass

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(C) Let the diameters of the three pipes be $d_1 = 1 	ext{ cm}$,$d_2 = 4/3 	ext{ cm}$,and $d_3 = 2 	ext{ cm}$.Since the amount of water flowing is

Vedclass · Accepted Answer

$36$

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(C) Let the diameters of the three pipes be $d_1 = 1 	ext{ cm}$,$d_2 = 4/3 	ext{ cm}$,and $d_3 = 2 	ext{ cm}$.Since the amount of water flowing is proportional to the square of the diameter,the rates of flow $R$ are $R_1 \propto 1^2$,$R_2 \propto (4/3)^2 = 16/9$,and $R_3 \propto 2^2 = 4$.Given that the largest pipe $(d_3 = 2 	ext{ cm})$ fills the cistern in $61 	ext{ minutes}$,its rate is $R_3 = 1/61$ of the cistern per minute.Since $R_3 = k \cdot 4 = 1/61$,the constant $k = 1/(61 	imes 4)$.Thus,$R_1 = 1 	imes k = 1/(61 	imes 4) = 1/244$ of the cistern per minute.$R_2 = (16/9) 	imes k = (16/9) 	imes (1/244) = 4/(9 	imes 61) = 4/549$ of the cistern per minute.Total rate when running together: $R_{total} = R_1 + R_2 + R_3 = \frac{1}{244} + \frac{4}{549} + \frac{1}{61}$.Converting to a common denominator ($244 = 4 	imes 61$ and $549 = 9 	imes 61$): $R_{total} = \frac{9 + 16 + 36}{36 	imes 61} = \frac{61}{36 	imes 61} = \frac{1}{36}$.Therefore,the cistern will be filled in $36 	ext{ minutes}$.

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