To find the percentage of votes in favor of the new speed limit, you can use the formula:
\[ \text{Percentage} = \left(\frac{\text{Number of votes in favor}}{\text{Total votes}}\right) \times 100 \]
In this case, the number of votes in favor is 114 and the total votes are 300:
\[ \text{Percentage} = \left(\frac{114}{300}\right) \times 100 \]
Now, calculate the fraction:
\[ \frac{114}{300} = 0.38 \]
Next, multiply by 100 to convert to a percentage:
\[ 0.38 \times 100 = 38 \]
So, the percentage of votes in favor of the new speed limit is:
\[ \boxed{38%} \]