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Answer 1

Answer:

Question :-

• There are two pipes in a water reservoirs of our school. Two pipes together take $\sf 11\dfrac{1}{9}$ minutes of fill the reservoirs. If the two pipes are opened separately, then one pipe would take 5 minutes more than the other pipe. Let us write by calculating, the time taken to fill the reservoir separately by each of the pipes.

Given :-

• There are two pipes in a water reservoirs of our school. Two pipes together take $\sf 11\dfrac{1}{9}$ minutes of fill the reservoirs. If the two pipes are opened separately, then one pipe would take 5 minutes more than the other pipe.

To Find :-

• The time taken to fill the reservoir separately by each of the pipes.

Solution :-

Let, the first pipe can fill the reservoir separately in x minutes.

And, the second pipe can fill the reservoir separately in (x + 5) minutes.

Now, in 1 minutes filled by 1st = $\sf \dfrac{1}{x}$ part.

And, in 1 minutes filled by 2nd = $\sf \dfrac{1}{x + 5}$ part

Then, by two filled in 1 minutes,

↦ $\sf \dfrac{1}{x} +\: \dfrac{1}{x + 5}$ part

↦ $\sf \dfrac{x + 5 + x}{x(x + 5)}$ part

↦ $\sf \dfrac{2x + 5}{x(x + 5)}$ part

➦ $\sf\bold{\green{\dfrac{2x + 5}{{x}^{2} + 5x}}}$ part

According to the question,

⇒ $\sf \dfrac{{x}^{2} + 5x}{2x + 5} =\: 11\dfrac{1}{9}$

⇒ $\sf \dfrac{{x}^{2} + 5x}{2x + 5} =\: \dfrac{100}{9}$

By doing cross multiplication we get,

⇒ $\sf 9({x}^{2} + 5x) =\: 100(2x + 5)$

⇒ $\sf 9{x}^{2} + 45x =\: 200x + 500$

⇒ $\sf 9{x}^{2} + 45x - 200x - 500 =\: 0$

⇒ $\sf 9{x}^{2} - 155x - 500 =\: 0$

⇒ $\sf 9{x}^{2} - (180 - 25)x - 500 =\: 0$

⇒ $\sf 9{x}^{2} - 180x + 25x - 500 =\: 0$

⇒ $\sf 9x(x - 20) + 25(x - 20) =\: 0$

⇒ $\sf (x - 20) (9x + 25) =\: 0$

⇒ $\sf x - 20 =\: 0$

➠ $\sf\bold{\pink{x =\: 20}}$

Either,

⇒ $\sf 9x + 25 =\: 0$

⇒ $\sf 9x =\: - 25$

➠ $\sf\bold{\pink{x =\: \dfrac{- 25}{9}}}$

We can't take time as negative (- ve).

So x will be 20.

Now, we have to find the total time taken to fill the reservoir separately.

$\mapsto$ The time taken by the first pipe to fill the reservoir,

➙ $\sf\bold{\purple{20\: minutes}}$

$\mapsto$ The time taken by the second pipe to fill the reservoir,

↛ $\sf (x + 5)\: minutes$

↛ $\sf (20 + 5)\: minutes$

➙ $\sf\bold{\purple{25\: minutes}}$

$\therefore$ The time taken by the first pipe to fill the reservoir separately is 20 minutes and the time taken by the second pipe to fill the reservoir separately is 25 minutes .