To solve this problem, let's denote the time it takes for the faster computer to complete the job on its own as \( x \) minutes.
We know that the slower computer takes 30 minutes to do the job on its own. We can express the work rates of both computers:
- The slower computer's work rate is \( \frac{1}{30} \) of the job per minute.
- The faster computer's work rate is \( \frac{1}{x} \) of the job per minute.
When both computers work together, their combined work rate is:
\[ \frac{1}{30} + \frac{1}{x} \]
According to the problem, together they can complete the job in 10 minutes. Therefore, their combined work rate can also be expressed as:
\[ \frac{1}{10} \text{ of the job per minute} \]
Setting these two expressions for the combined work rate equal gives us the equation:
\[ \frac{1}{30} + \frac{1}{x} = \frac{1}{10} \]
To solve for \( x \), we first find a common denominator for the left side of the equation. The common denominator of 30 and \( x \) is \( 30x \).
Rewriting the equation gives:
\[ \frac{x}{30x} + \frac{30}{30x} = \frac{3x}{30x} \]
This simplifies to:
\[ \frac{x + 30}{30x} = \frac{1}{10} \]
Next, we cross-multiply:
\[ 10(x + 30) = 30x \]
Expanding the left side:
\[ 10x + 300 = 30x \]
Rearranging gives:
\[ 300 = 30x - 10x \] \[ 300 = 20x \]
Dividing both sides by 20:
\[ x = \frac{300}{20} = 15 \]
Thus, the faster computer can complete the job on its own in \( 15 \) minutes.
Final answer: 15 minutes.