a) 28 minutes are taken to have the same amount of water.
b) Both pools have an amount of 1134 liters when 28 minutes have passed.
a) Physically speaking, the capacity ([tex]Q[/tex]) of each pool, in liters, is equal to the product of flow rate ([tex]\dot Q[/tex]), in liters per minute, and time ([tex]t[/tex]), in minutes. Hence, we derive the following functions for each pool:
[tex]Q_{1} = 567 + 20.25\cdot t[/tex] (1)
[tex]Q_{2} = 40.5\cdot t[/tex] (2)
The time needed to find both pools with the same amount of water is found by the following expression:
[tex]Q_{1} = Q_{2}[/tex] (3)
By (1) and (2) in (3):
[tex]567 + 20.25\cdot t = 40.5\cdot t[/tex]
[tex]20.25\cdot t = 567[/tex]
[tex]t = 28\,min[/tex]
28 minutes are taken to have the same amount of water. [tex]\blacksquare[/tex]
b) By (2) and knowing that [tex]t = 28\,min[/tex], then we have the corresponding amount:
[tex]Q_{2} = 40.5\cdot (28)[/tex]
[tex]Q_{2} = 1134\,L[/tex]
Both pools have an amount of 1134 liters when 28 minutes have passed. [tex]\blacksquare[/tex]
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