https://gyazo.com/74f60d63c5d038c50923779a3a06edc8

I derived this equation

x = time milk is added
y = temperature below which not adding milk at all would be quicker than adding milk at time (x) I.E if you want it to cool down to 30 degrees and y = 35 degrees then it would be quicker not to add milk
T_r = room temperature
T_c = Temperature of coffee when it is poured
T_m = Temperature of milk
K = Mass of coffee divided by the mass of milk added
a = constant to be found

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It takes into account

The change in temperature from the addition of milk

The change in the rate of cooling due to the addition of milk

The change in the rate of cooling due to the increased mass of the coffee