Louis ran to Versailles and then walked back to town. His running rate was 6 kilometers per hour and his walking rate was 3 kilometers per hour. How far was it to Versailles if the round trip took 6 hours?

1. Given the total time for the round trip is 6 hours, express the individual times:

\text{Time to run to Versailles} = \frac{x}{6} \, \text{hours}

\text{Time to walk back to town} = \frac{x}{3} \, \text{hours}

2. The equation for the total time is:

\frac{x}{6} + \frac{x}{3} = 6

3. Find a common denominator to combine fractions:

\frac{x}{6} + \frac{2x}{6} = 6

4. Simplify the equation:

\frac{3x}{6} = 6

\frac{x}{2} = 6

5. Solve for \( x \):

x = 12

6. Therefore, the distance to Versailles is:

x = 12 \, \text{km}