Answer:
9 minutes
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.
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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.