A tank is filled by three pipes with uniform | vedclass

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(C) Let the time taken by the second pipe to fill the tank be $x$ hours.Then,the time taken by the first pipe is $x+5$ hours,and the time taken by the

Vedclass · Accepted Answer

$15$

Vedclass · Answer

(C) Let the time taken by the second pipe to fill the tank be $x$ hours.Then,the time taken by the first pipe is $x+5$ hours,and the time taken by the third pipe is $x-4$ hours.According to the problem,the first two pipes working together fill the tank in the same time as the third pipe alone.Therefore,the rate of the first pipe plus the rate of the second pipe equals the rate of the third pipe:$\frac{1}{x+5} + \frac{1}{x} = \frac{1}{x-4}$$\frac{x + (x+5)}{x(x+5)} = \frac{1}{x-4}$$\frac{2x+5}{x^2+5x} = \frac{1}{x-4}$$(2x+5)(x-4) = x^2+5x$$2x^2 - 8x + 5x - 20 = x^2 + 5x$$2x^2 - 3x - 20 = x^2 + 5x$$x^2 - 8x - 20 = 0$$(x-10)(x+2) = 0$Since time cannot be negative,$x = 10$ hours.The time required by the first pipe is $x+5 = 10+5 = 15$ hours.

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