Final answer:
To calculate the tank's capacity, the rates at which the pipes can fill the tank are determined and combined. All three pipes together fill the tank at the rate of 1/15 tanks per minute. Comparing this rate to the waste pipe's emptying rate reveals an inconsistency, as none of the provided answer choices match the calculated capacity of 120 gallons.
Step-by-step explanation:
To find the capacity of the tank, we first need to calculate the rates at which the pipes can fill the tank. The first pipe fills the tank in 20 minutes, so its rate is 1/20 of the tank per minute. The second pipe fills it in 24 minutes, meaning its rate is 1/24 of the tank per minute.
If the pipes work together, minus the waste pipe, their combined rate would be (1/20 + 1/24) tanks per minute. To find the least common denominator (LCD), we use 120, so the combined rate would be (6/120 + 5/120) = 11/120 tanks per minute.
Since all three pipes together fill the tank in 15 minutes, the tank's rate of filling is 1/15 tanks per minute. Therefore, the waste pipe's rate is the difference between the combined filling rate and the three-pipe filling rate: (11/120) – (1/15) = (11/120) – (8/120) = 3/120 or 1/40 tanks per minute.
The waste pipe can empty 3 gallons per minute which is 1/40 of the tank per minute; thus, the capacity of the tank is 40 times 3 gallons, which is 120 gallons. However, this option is not listed in the question choices, possibly due to a typo or mistake in the question. Therefore, an error is present in this question, and none of the given answers (a to d) are correct based on the calculations.