Answer:
42 6/7 minutes
Step-by-step explanation:
Each minute, the first pump adds 1/50 of a tank; the second pump adds 1/60 of a tank; and the third pump subtracts 1/75 of a tank. Then, each minute the total amount added is ...
... (1/50) + (1/60) - (1/75) = 6/300 + 5/300 - 4/300
... = 7/300 . . . . of a tank.
Then in 300/7 minutes, or 42 6/7 minutes, the tank will be full.
Using the together rate, it is found that the 3 pumps together would fill the tank in 42.86 minutes.
The together rate is given by the sum of each separate rate.
In this problem, the rates are given by: 1/50, 1/60 and -1/75.
Hence, the together rate is given by:
[tex]\frac{1}{x} = \frac{1}{50} + \frac{1}{60} - \frac{1}{75}[/tex]
Applying the least common multiple:
[tex]\frac{1}{x} = \frac{6 + 5 - 4}{300}[/tex]
[tex]7x = 300[/tex]
[tex]x = \frac{300}{7}[/tex]
[tex]x = 42.86[/tex]
Hence, it is found that the 3 pumps together would fill the tank in 42.86 minutes.
More can be learned about the together rate at https://brainly.com/question/25159431
