A pipe fills a water tank three times faster | vedclass

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Question

(D) Let the time taken by the faster pipe to fill the tank be $x$ minutes. Since the other pipe is three times slower,it will take $3x$ minutes to fil

Vedclass · Accepted Answer

$2$ hours $24$ minutes

Vedclass · Answer

(D) Let the time taken by the faster pipe to fill the tank be $x$ minutes. Since the other pipe is three times slower,it will take $3x$ minutes to fill the tank. The work done by the faster pipe in $1$ minute is $\frac{1}{x}$ and by the slower pipe is $\frac{1}{3x}$. Given that together they fill the tank in $36$ minutes,their combined work rate is $\frac{1}{36}$. Therefore,$\frac{1}{x} + \frac{1}{3x} = \frac{1}{36}$. Multiplying by $3x$,we get $3 + 1 = \frac{3x}{36}$,which simplifies to $4 = \frac{x}{12}$. Thus,$x = 48$ minutes. The slower pipe takes $3x = 3 	imes 48 = 144$ minutes. $144$ minutes is equal to $2$ hours and $24$ minutes.

$A$ pipe fills a water tank three times faster than another pipe. If the two pipes together can fill the empty tank in $36$ $minutes$,then how much time will the slower pipe alone take to fill the tank?

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