#### Answer

5 liters of pure alcohol must be added to the solution.

#### Work Step by Step

Let x represent the amount of pure alcohol that must be added.
We can use the following guideline to solve this problem:
Original amount of alcohol + Amount of alcohol added = Final amount of alcohol.
Original amount of alcohol = 20% $\times$ 15 = 0.2 $\times$ 15 = 3 liters.
Amount of alcohol added = x
Final amount of alcohol = 40% $\times$ (15 + x) = 0.4 $\times$ (15 + x) = 6 + 0.4x
Substitute these values into the equation to obtain:
3 + x = 6 + 0.4x
0.6x = 3
Divide both sides by 0.6
x = 5
5 liters of pure alcohol must be added to the solution.