It is not so much a question of time as of quantities of heat and of heat flow along gradients of temperature. The cooler the ice cubes the more heat they can absorb apart from how much latent heat of melting they can absorb. The hotter the water the faster it will convey its heat by conduction and convestion, and the more heat it can contribute to the ice or the ice-cooled water. The hotter the surrounding air, the faster it will heat the water, causing the ice to melt correspondingly faster.

Your question is rather like asking how long it will take  a car to roll downhill if one adds more weight to the vehicle or increases the slope; there are so many variables such as rolling resistance and the state of the road surface and tyres, that the question is not directly answerable, even if one knows the mass of the car and the height of the hill.

This space to let!

The

heat transfer from a liquid to its solid form (called "melting")

is very fast.

In practice it is limited by the speed with which the melted

cold water is mixed with the rest.

So stirring and the surface area of the ice are the most important factor.

Under typical conditions of a drink, all other factors like

the temperature of the ice (blelow zero C) and so on

are secondary. The heat of melting for ice is 80 cal/g ,

whereas the specific heat of ice 0 .5 cal/gdeg is small,

and the heat conduction from inside the ice cube is slow.

So a ice cube of 1 g and say, - 10 degrees C supplies 5 cal when

heated from -10 to 0 degrees, whereas the same amount of ice will 

take on 80 cal when melting at 0 degrees!

The melting occurs instantously at the surface,

the heat taken from the liquid is limited by the

dispersion of the melted ice into the drink.

Georg