In winter, people play hockey on Alta Lake in Whistler. However, it is not considered safe to play hockey on ice until the ice is 20 cm thick.

In winter, people play hockey on Alta Lake in Whistler. However, it is not considered safe to play hockey on ice until the ice is 20 cm thick. On a winter day with a temperature −10◦C, it is observed that the lake has a 1cm thick layer of ice over the entire surface. Assuming the temperature stays constant, find how long it will take for the ice to be safe: (a) If the air temperature remains at −10◦C, find the rate in cm per hour at which ice is added to the layer. The thermal conductivity of ice is 2.18W/m·K. (b) Find the time that the ice layer reaches a thickness of 20 cm.