Need help please help

  9 minutes

Step-by-step explanation:

The water volume in pool 1 starts at 50 gallons and increases at 2.3 gallons per minute. An expression for that volume could be ...

  v = 50 +2.3t

The water volume in pool 2 starts at 102.2 gallons and decreases at 3.5 gallons per minute. An expression for that volume could be ...

  v = 102.2 -3.5t

The volumes will be equal when ...

  50 +2.3t = 102.2 -3.5t

  5.8t = 52.2 . . . . . . . . . . . subtract 50-3.5t from both sides

  t = 52.2/5.8 = 9 . . . . . . . divide by the coefficient of t

After 9 minutes, the pools will contain the same amount of water.

The equation 5.8t = 52.2 tells you the 52.2 gallon difference in volumes is being reduced at the rate of 5.8 gallons per minute. You don't really need the 'v' equations to figure that out.