Calculate Thickness of Ice Sheet on Lake: -17.8°C in 3.80 Minutes

[rlc]

Homework Statement

A 0.315-m-thick sheet of ice covers a lake. The air temperature at the ice surface is -17.8 °C. In 3.80 minutes, the ice thickens by a small amount. Assume that no heat flows from the ground below into the water and that the added ice is very thin compared to 0.315 m. Calculate the number of millimeters by which the ice thickens.

Homework Equations

Q = k A ΔT / d
dQ/dt = k∙A∙∆T/∆x
The heat of fusion of water is about 334 kJ / kg
k thermal conductivity, for ice k = 2.33 Wm⁻¹K⁻¹
A surface area of the lake
∆T temperature difference between the two sides of the ice sheet
∆x thickness of the ice sheet

The Attempt at a Solution

I've tried a bunch of different equations, but I'm missing something. Is that equation the one to use?

 

[rlc]

Never mind, I figured it out:
Density of ice=917 kg/m^3
Lf=33.5E4 J/kg
Thermal conductivity ice=2.2 J/smdegC

h=k(deltaT)t/pLfL
h=(2.2)(17.8)(228 secs)/(917)(33.5E4)(0.315)
h=9.2268E-5 m
Multiply by 1000 to get mm
0.0923 mm