We can use a ratio to solve this question. Lets refer to the amount formed by the formula as a serving
1 serving needs 3/8 gal
We want to create 7/9 servings extra, so
1 + 7/9 = 16/7
1 : 3/8
16/7 : x
1/(3/8) = (16/7) / x
8 / 3 = 16x / 7
x = 7/6
He needs to use 7/6 gallons of water.
