Question

Two taps together can fill a tank completely in 3×1÷13 minutes. The smaller tap takes three minutes more than the bigger tab 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

Step By Step Explaination:-

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

So, the work done by bigger pipe in one minute = \frac{1}{x}x1

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}x+31

Thus, their combined work in one minute = \frac{1}{x}+\frac{1}{x+3}x1+x+31

∵ When they work together they took 3\frac{1}{13}3131minutes.

Their combined work in one minute = \frac{1}{3\frac{1}{13}}=\frac{1}{\frac{40}{13}}=\frac{13}{40}31311=13401=4013

\implies \frac{1}{x}+\frac{1}{x+3} = \frac{13}{40}⟹x1+x+31=4013

\frac{x+3+x}{x(x+3)}=\frac{13}{40}x(x+3)x+3+x=4013

\frac{2x+3}{x^2+3x}=\frac{13}{40}x2+3x2x+3=4013

80x+120 = 13x^2 + 39x80x+120=13x2+39x

13x^2 -41x - 120=013x2−41x−120=0

13x^2 - 65x + 24x - 120=013x2−65x+24x−120=0

13x(x-5)+24(x-5)=013x(x−5)+24(x−5)=0

(13x+24)(x-5)=0(13x+24)(x−5)=0

13x + 24 =0\text{ or }x-5=013x+24=0 or x−5=0

\implies x = -\frac{24}{13}\text{ or }x=5⟹x=−1324 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,