one inlet pipe can fill an empty pool in 16 hours, a drain can empty the pool in 20 hours.

Question

how long will it take the pipe to fill the pool if the drain is left open? t= time to fill

Answer 1

We need to write an equation that represents the how much of the pool is filled; "y" will refer to how much of the pool is filled, and "t" will represent the number of hours that have passed.

 

The pool can fill in 16 hours, and it can empty in 20 hours. Therefore, in one hour, ¹/₁₆ of the pool can be filled, and ¹/₂₀ of the pool can be emptied.

 

 

 

In this scenario, for every hour, we will be adding ¹/₁₆ of the pool water while subtracting ¹/₂₀ of the pool water.

 

Therefore:

y = ¹/₁₆ t - ¹/₂₀ t

y = ⁵/₈₀ t - ⁴/₈₀ t

y = ¹/₈₀ t

 

There is our equation. We want the pool to be completely filled. Because "y" represents how much of the pool is filled, the way you would express that numerically is "1" (in other words, 1 whole pool --- as opposed to a fraction of the pool).

 

1 = ¹/₈₀ t

t = 80 hours