The math is fairly simple. You know for how much concentrated cold brew you will be using that it is at a ratio of 1:4. Since the resulting concentration of the cold brew is constant (since it has already been brewed) we only really care about the parts of water that are in it; 4 parts.
Therefore to calculate how much water you need to add to dilute your 1:4 concentrate into a 1:15 cup, divide the amount of concentrate you are using by 4 and then multiply that by the remaining parts you wish to add, which is
15 - 4 = 11 which gives you the amount of water you need to add in whatever units you measured the amount of concentrate you started with.
Using your example numbers:
Start with 100g of cold brew concentrate at 1:4 ratio. Each part of water is therefore
100/4 = 25g. The amount of water you will need to add is therefore
11 x 25g = 275g to result in a total amount of 375g in your final cup.
Check the final answer by doing a reverse calculation. If the concentrate is 1:4 and you have 100g of it, it means you started with 25g of ground coffee. Therefore making a 1:15 ratio cup of coffee with 25g of coffee means
25g x 15 = 375g of water must be added.
The answers align.
For an amount of cold brew to be diluted,
c units, which has a coffee-to-water ratio of
1:n, the amount of each part of water in the cold brew,
c/n. The amount of water to be added to achieve a final ratio of
1:m is therefore
w x (m-n) units.
Units are any form of measure of the liquid mass being used, in g, mL or others.