To solve the equation \( \frac{1}{3}k + \frac{1}{4}k = 1 \), we first find a common denominator for the fractions on the left side. The least common multiple of 3 and 4 is 12.
Rewriting the fractions with the common denominator:
\[ \frac{1}{3}k = \frac{4}{12}k \] \[ \frac{1}{4}k = \frac{3}{12}k \]
Now, we can substitute these back into the equation:
\[ \frac{4}{12}k + \frac{3}{12}k = 1 \]
Combining the fractions:
\[ \frac{4 + 3}{12}k = 1 \] \[ \frac{7}{12}k = 1 \]
To solve for \( k \), we multiply both sides by the reciprocal of \(\frac{7}{12}\):
\[ k = 1 \cdot \frac{12}{7} \]
Therefore, the value of \( k \) is:
\[ k = \frac{12}{7} \]
So the final answer is \( \frac{12}{7} \).