Smelte isen?

We consider a circular lake with a radious of 1.0 km covered in 5 mm of ice. 169 mm of rain will fall over 24 hours, and we make the apporcimation that it falls at a constant rate. 

The rain on earth consist of water and has a temperatur of 4.0ºC, the ice is water-ice and has a temperature of -1.0º C. We ignore the heat lost the surroundings and assumen that the transfer of heat is instaneous. How much time will pass before the ice is melted entirely? 

Brugbar info: 

Heat of fusion of water: 334 J/g

Specific heat of ice = 250 j/kg · K

Specifik heat of water = 4.18 J/g · ºC

Density of ice = 917 kg/m³

Density of water = 999.99 kg/m³

Area of circle A_lake = π · r² = π · 1000² m² = 314159.7 m²

Density = mass/ Volume

V_ice = 314159.7 m²  · 0.005 m = 157079.6 m³

mass_ice = Density · Volume = 999.79 kg/m³ · 157079.6 m³ = 157046613,2 kg = 157046613.2 · 10³g

V_rain = 314159.7 m2  · 0.169 m = 530929.17 m³

mass_rain = Density · Volume = 999.79 kg/m3 · 530929.17 m³ = 530928629.1 kg = 530928629.1 · 10³g

For at finde den total energi der bruges til at smelte iset, er jeg nød til at kende summet af to energier: 

Q₁ = mcΔT og Q₂ = mL_f => Q = Q₁ + Q₂

Har regnet noget af opgaven men er gået i stå. Det jeg har regnet, har jeg skrevet med. Kan simpelthen ikke få min Q₁ og Q₂ til at passe. Skal desuden finde den tid det tager før at hele isen er smeltet?? HJÆLP??