Solution:

Given:
Initial temperature of ice, T1 = -10°C
Room temperature, T2 = 25°C
Reduction in temperature per hour, dT/dt = -5°C/hour

To find:
Total time required to freeze the ice, t

Approach:
The temperature difference between the ice and the room should be maintained until the ice freezes. We can calculate the time required to lower the temperature of the room to the freezing point of water, and then the time required to freeze the ice.

Calculation:
The freezing point of water is 0°C, so the temperature difference between the ice and the room is:
ΔT = T2 - T1
ΔT = 25 - (-10)
ΔT = 35°C

The time required to lower the temperature of the room to the freezing point of water is:
t1 = ΔT / dT/dt
t1 = 35 / 5
t1 = 7 hours

After 7 hours, the room temperature would be 0°C. The ice would still be at -10°C.

The time required to freeze the ice can be calculated using the specific heat of ice and the latent heat of fusion of water.

The specific heat of ice is 2.1 J/g°C.
The latent heat of fusion of water is 334 J/g.

To freeze 1 g of ice at -10°C, we need to:
1. Raise the temperature of the ice from -10°C to 0°C, which requires:
Q1 = m * c * ΔT
Q1 = 1 * 2.1 * 10
Q1 = 21 J

2. Convert the ice at 0°C to water at 0°C, which requires:
Q2 = m * Lf
Q2 = 1 * 334
Q2 = 334 J

The total heat required to freeze 1 g of ice is:
Q = Q1 + Q2
Q = 21 + 334
Q = 355 J

The mass of ice in the ice factory is not given. Therefore, we cannot calculate the time required to freeze the ice.

Conclusion:
The time required to lower the temperature of the room to the freezing point of water is 7 hours. The time required to freeze the ice depends on the mass of ice in the ice factory.