Tarik can complete a job in 12 minutes. If Andy helps Tarik, they can complete the job in 4 minutes.
How long would it take for Andy to complete the job on his own?

Answer

To solve the problem, we will follow these steps:

### Step 1: Define Variables
Let \( X \) be the time (in minutes) that Andy takes to complete the job on his own.

### Step 2: Determine Tarik's Work Rate
Tarik can complete the job in 12 minutes. Therefore, in one minute, Tarik completes:
\[ \frac{1}{12} \text{ of the job} \]

### Step 3: Determine Andy's Work Rate
If Andy takes \( X \) minutes to complete the job, then in one minute, he completes:
\[ \frac{1}{X} \text{ of the job} \]

### Step 4: Combined Work Rate
When both Tarik and Andy work together, they can complete the job in 4 minutes. Thus, in one minute, they complete:
\[ \frac{1}{4} \text{ of the job} \]

### Step 5: Set Up the Equation
The combined work rate of Tarik and Andy can be expressed as:
\[ \frac{1}{12} + \frac{1}{X} = \frac{1}{4} \]

### Step 6: Solve for \( X \)
To solve for \( X \), first isolate \( \frac{1}{X} \):
\[ \frac{1}{X} = \frac{1}{4} - \frac{1}{12} \]

### Step 7: Find a Common Denominator
The least common multiple of 4 and 12 is 12. Rewrite the fractions:
\[ \frac{1}{4} = \frac{3}{12} \]
So,
\[ \frac{1}{X} = \frac{3}{12} - \frac{1}{12} = \frac{2}{12} \]

### Step 8: Simplify
Simplifying \( \frac{2}{12} \) gives:
\[ \frac{1}{X} = \frac{1}{6} \]

### Step 9: Solve for \( X \)
Taking the reciprocal of both sides gives:
\[ X = 6 \]

### Conclusion
Thus, Andy would take **6 minutes** to complete the job on his own.

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