Answer
8.7 hours.
Work Step by Step
The heat conducted into the box is the latent heat of fusion of the ice, $Q=m_{ice}L_f$.
The heat is conducted through the total area of the box’s six surfaces, and the length of the conducting material is the thickness of the foam sides.
Find the surface area A
$$A=2(0.25m)(0.35m)+2(0.35m)(0.55m)+2(0.25m)(0.55m)=0.835m^2$$
Calculate the rate of heat flow using equation 14–5.
$$\frac{Q}{t}=kA\frac{T_1-T_2}{\mathcal{l}}$$
Solve for the time. Use twice the thermal conductivity of air for the foam's conductivity.
$$t= \frac{ m_{ice}L_f \mathcal{l} }{kA\Delta T}$$
$$t= \frac{ (8.2kg)(3.33\times10^5 J/kg)(0.015m)}{2(0.023 ) (0.835m^2)(34C)}\approx3.1\times10^4 s\approx 8.7 h$$