Question

two taps together can fill tank completely in 3 1/13 minutes. The smaller tap takes 3 minutes more than the bigger tap to fill the tank. How much time does each tap take to fill the tank completely?​

Answer 1

Answer:

Bigger pipe takes 5 minutes and smaller pipe takes 8 minutes

Step-by-step explanation:

Let x be the number of minutes taken by bigger pipe,

So, the work done by bigger pipe in one minute = $\frac{1}{x}$

Then according to the question,

Time taken by smaller pipe = (x + 3) minutes,

So, the work done by smaller pipe in one minute = $\frac{1}{x+3}$

Thus, their combined work in one minute = $\frac{1}{x}+\frac{1}{x+3}$

∵ When they work together they took $3\frac{1}{13}$ minutes.

Their combined work in one minute = $\frac{1}{3\frac{1}{13}}=\frac{1}{\frac{40}{13}}=\frac{13}{40}$

$\implies \frac{1}{x}+\frac{1}{x+3} = \frac{13}{40}$

$\frac{x+3+x}{x(x+3)}=\frac{13}{40}$

$\frac{2x+3}{x^2+3x}=\frac{13}{40}$

$80x+120 = 13x^2 + 39x$

$13x^2 -41x - 120=0$

$13x^2 - 65x + 24x - 120=0$

$13x(x-5)+24(x-5)=0$

$(13x+24)(x-5)=0$

$13x + 24 =0\text{ or }x-5=0$

$\implies x = -\frac{24}{13}\text{ or }x=5$

∵ Number of minutes can not be negative,

Hence, the time taken by bigger pipe = 5 minutes,

And, the time taken by smaller pipe = 5 + 3 = 8 minutes,

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