A sludge pool is filled by two inlet pipes. One pipe can fill the pool in 14 days and the other pipe can fill it in 22 days. However, if no sewage is added, waste removal will empty the pool in 35 days. How long will it take the two inlet pipes to fill an empty pool? answer

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To find out how long it will take for the two inlet pipes to fill an empty pool, we need to consider their individual rates of filling the pool and the rate at which waste is being removed.

Let's denote the rate at which the first inlet pipe fills the pool as "x" and the rate at which the second inlet pipe fills the pool as "y". We can determine their rates by calculating the fraction of the pool filled per day.

The first pipe fills the pool in 14 days, so its rate is 1/14 of the pool per day (1 pool / 14 days = 1/14 pool/day).
The second pipe fills the pool in 22 days, so its rate is 1/22 of the pool per day (1 pool / 22 days = 1/22 pool/day).

The rate at which the waste removes water from the pool is determined by the time it takes to empty the pool, which is 35 days. So the waste removal rate is 1/35 of the pool per day (1 pool / 35 days = 1/35 pool/day).

Now, let's consider the net rate at which the pool is being filled per day. It is given by the sum of the rates of the two inlet pipes minus the rate of waste removal:
Net rate = x + y - (1/35)

Since we want to find how long it will take for the two inlet pipes to fill an empty pool, we know that when the pool is full, the net rate should be equal to 1 pool per day.

Hence, we can set up the equation:
x + y - (1/35) = 1

To solve for x + y, we rearrange the equation:
x + y = 1 + (1/35)

x + y = 36/35

Now, we have the sum of the rates of the two inlet pipes, x + y, but we need to find how long it will take for them to fill the pool. Let's denote this time as "t" (in days).

Since the rate is equal to the amount filled per day, we can set up the equation:
t * (x + y) = 1

Substituting the value we found for x + y:
t * (36/35) = 1

Simplifying the equation:
(36/35) * t = 1

To solve for t, we isolate it:
t = 35/36

So, it will take approximately 35/36 of a day for the two inlet pipes to fill an empty pool.

However, since time is typically measured in whole numbers, we need to convert this to the nearest whole number.

Taking the nearest whole number, it will take 1 day for the two inlet pipes to fill an empty pool.