Students on a spring break picnic bring a cooler that contains 5.1 kg of ice at 0.0 °C. The cooler has walls that are 3.8 cm thick and are made of Styrofoam, which has a thermal conductivity of 0.030 W / (m ( C°). The surface area of the cooler is 1.5 m2, and it rests in the shade where the air temperature is 21 °C.

(a) Find the rate at which heat flows into the cooler.

(b) How much time does it take for the ice in the cooler to melt?