The quantity of water needed to be mixed with ½ gallon of chemical is 3 gallons.
How much water would be mixed with 1/2 gallon of the chemical?
Chemical : water = 1 : 6
let
quantity of water needed = x
So,
1 : 6 = 1/2 : x
1/6 = 1/2 ÷ x
1/6 = 1/2 × 1/x
1/6 = 1/2x
cross product
1 × 2x = 6 × 1
2x = 6
Divide both sides by 2
x = 6/2
x = 3 gallons
Hence, 3 gallons of water is required.