what is the rate that cold water reaches ambient temperature if water is 40 deg and temp is 90deg?

Answer 1

It is generally proportional to the difference in temperature, not the square of the difference. Since the difference is constantly changing as the water warms up, this is an exponential problem in which the current temperature T theoretically approaches but never reaches the ambient temperature T1.
The describing equation is T = T0 + (T1 - T0) * e^(-t/k), where T0 is initial temperature (40), T1 is ambient temperature (90), t is the time the water has been exposed to the ambient temperature, and k is the time constant of the temperature change (which is primarily governed by water mass and surface area in addition to factors such as air speed and those mentioned in answer 1). What this equation says is that in k seconds, T has approached T1 to within 1/e times (T1 - T0), in 2k seconds to within 1/e^2, etc.

Answer 2

The rate is not constant. It is proportional to the square of the temp differences.
If you want to look at this in more detail you have to consider the drop in temperatute sorounding the cold water. Then it will take longer. you have to conside the heat flow in the air etc.