A new unit of length is chosen such that the speed of light is vacuum is unity. What is the distance between the sun and the Earth in terms of the new unit if light takes 8 min and 20 s to cover this distance?

Explanation

To solve the problem, we need to determine the distance between the Sun and the Earth in a new unit of length where the speed of light is defined as unity (1 unit per second). The time taken for light to travel this distance is given as 8 minutes and 20 seconds.

### Step-by-Step Solution:

1. **Convert Time to Seconds**:
- The time taken for light to travel from the Sun to the Earth is given as 8 minutes and 20 seconds.
- We first convert this time into seconds.
- Calculation:
\[ \text{Total time in seconds} = (8 \text{ minutes} \times 60 \text{ seconds/minute}) + 20 \text{ seconds} = 480 + 20 = 500 \text{ seconds} \]

2. **Define the Speed of Light**:
- In the new unit system, the speed of light is defined as unity, which means:
\[ \text{Speed of light} = 1 \text{ unit/second} \]

3. **Calculate the Distance**:
- The distance can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Substituting the values we have:
\[ \text{Distance} = 1 \text{ unit/second} \times 500 \text{ seconds} = 500 \text{ units} \]

4. **Conclusion**:
- Therefore, the distance between the Sun and the Earth in the new unit of length is:
\[ \text{Distance} = 500 \text{ new units of length} \]

### Final Answer:
The distance between the Sun and the Earth is 500 new units of length.