While Greg was solving the work rate question above, he subtracted the rate at which the pool was being filled from the rate at which water was exiting the pool, that is (b-225). I want to know why he did this and not rather subtract the rate at which water was exiting the pool from the rate at which the pool was being filled, that is (225-b).
I would assume because the question is asking about the rate of the water exiting the pool.
Both 225 - b and b - 225 work; it’s just that your physical interpretation of the net rate must change accordingly
Does that mean the formula changes based on what is being asked?
Alright. I used (225-b) in solving the problem and i got b=112.5gallons/hour. How can i interpret this value in order to arrive at the correct answer?
Since the tank is emptying despite the constant influx of water (225 gallons/hour), the actual (or gross) rate of discharge must be greater than 225.
The value of b (in your answer) represents the net rate of discharge, while already accounting for the inflow as well.
To get the actual rate of discharge, add b to the rate of inflow:
b + 225 = 337.5
This might seem a bit confusing, so I’d suggest sticking with the same physical principle throughout the question.
In particular, your equation should be constructed as follows:
-1350 = (225 - b)(12), where 1350 is negative because it represents a loss of 1350 gallons.
The first explanation is indeed confusing. The second one is understandable and settles me well. Thanks for the help.