A large pipe can fill a tank in 6 hours less than it takes the small pipe. Working together, they can fill it in #4# hours. How long would it take the small pipe to fill the tank if it was working alone?

Answer 1
Let the time it takes to fill the smaller pipe be #x# and the time it takes the larger pipe be #x - 6#.
Then, the amount of tank that can be filled in #1# hour is:
#1/x + 1/(x - 6) = 1/4#

Solve this equation.

#(4(x - 6))/(4x(x - 6)) + (4(x))/(4x(x - 6)) = (x(x - 6))/(4(x)(x - 6))#

We can now eliminate the denominators.

#4x - 24 + 4x = x^2 - 6x#
#0 = x^2 - 14x + 24#
#0 = (x - 12)(x - 2)#
#x = 12 and 2#
Two solutions may seem non sensical, but if you determine the length of time it takes using the large pipe, you will get #6# and #-4#. A negative answer is not possible, so we discredit #x = 2#.
So, it takes the small pipe #12# hours to fill the tank.

Hopefully this helps!

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Answer 2

Let ( x ) represent the number of hours it takes for the small pipe to fill the tank alone.

The large pipe takes ( x - 6 ) hours to fill the tank alone.

When they work together, their combined rate is the sum of their individual rates. Therefore, the combined rate is ( \frac{1}{x} + \frac{1}{x-6} ).

Given that they can fill the tank together in 4 hours, their combined rate is ( \frac{1}{4} ).

Setting up the equation ( \frac{1}{x} + \frac{1}{x-6} = \frac{1}{4} ), solve for ( x ) to find the time it takes for the small pipe to fill the tank alone.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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