Answer:10 minutes
Step-by-step explanation:The amount of water in Pool A after t minutes can be represented by the function A(t) = 380 - 9t, where 9t is the amount of water lost due to the leak. The amount of water in Pool B after t minutes can be represented by the function B(t) = 420 - 13t, where 13t is the amount of water lost due to the leak.
To find when the two pools have the same amount of water, we need to solve the equation A(t) = B(t):
380 - 9t = 420 - 13t
4t = 40
t = 10
Therefore, the two pools will have the same amount of water after 10 minutes. To find how much water will be in the pools at that time, we can substitute t = 10 into either A(t) or B(t):
A(10) = 380 - 9(10) = 290
B(10) = 420 - 13(10) = 290
Therefore, both pools will have 290 gallons of water after 10 minutes.