Introduction:
Temperature plays a crucial role in the spoilage of orange juice. In this scenario, we are given that at room temperature (20°C), orange juice gets spoilt in about 64 hours. However, when stored in a refrigerator at 3°C, the juice can be stored three times as long before it spoils. We need to determine how long it would take for the juice to spoil at 40°C.

Given Information:
- Room temperature: 20°C
- Spoilage time at room temperature: 64 hours
- Refrigerator temperature: 3°C
- Juice can be stored three times as long in a refrigerator before spoiling

Calculating Spoilage Time at 3°C:
To calculate the spoilage time at 3°C, we need to consider that the juice can be stored three times as long compared to room temperature. Therefore, the spoilage time at 3°C would be 64 hours multiplied by 3, which equals 192 hours.

Determining the Rate of Spoilage:
To determine the rate of spoilage, we can divide the spoilage time by the temperature difference between the two scenarios. In this case, the temperature difference is 20°C (room temperature) minus 3°C (refrigerator temperature), which equals 17°C.

The rate of spoilage can be calculated as follows:
Rate of spoilage = Spoilage time / Temperature difference
Rate of spoilage = 192 hours / 17°C
Rate of spoilage ≈ 11.29 hours/°C

Calculating Spoilage Time at 40°C:
Now that we have the rate of spoilage, we can calculate the spoilage time at 40°C. We need to determine the temperature difference between 40°C and the reference temperature of 3°C, which is 40°C - 3°C = 37°C.

Using the rate of spoilage, we can calculate the spoilage time at 40°C as follows:
Spoilage time at 40°C = Rate of spoilage * Temperature difference
Spoilage time at 40°C ≈ 11.29 hours/°C * 37°C
Spoilage time at 40°C ≈ 417.73 hours

Conclusion:
At a temperature of 40°C, orange juice would take approximately 417.73 hours to spoil. It is important to note that these calculations are based on the assumption of a linear relationship between temperature and spoilage rate. In reality, spoilage rates may vary depending on other factors such as pH, sugar content, and microbial activity.