White can do a job in 15 days and Lee can do the same job in 9 days. With the help of Scott, they did the job in 3 days only. Then, Scott alone can do the job in

Options

A. `6^(1//5)` days
B. `6^(2//5)` days
C. `6^(3//7)` days
D. 10 days

Answer

To solve the problem, we need to find out how long Scott alone would take to complete the job given the work rates of White, Lee, and Scott working together.

### Step-by-Step Solution:

1. **Determine the work rates of White and Lee:**
- White can complete the job in 15 days. Therefore, White's work rate is:
\[ \text{Work rate of White} = \frac{1}{15} \text{ jobs per day} \]
- Lee can complete the job in 9 days. Therefore, Lee's work rate is:
\[ \text{Work rate of Lee} = \frac{1}{9} \text{ jobs per day} \]

2. **Calculate the combined work rate of White and Lee:**
- The combined work rate of White and Lee is:
\[ \text{Combined work rate of White and Lee} = \frac{1}{15} + \frac{1}{9} \]
- To add these fractions, we need a common denominator. The least common multiple (LCM) of 15 and 9 is 45.
- Convert each fraction:
\[ \frac{1}{15} = \frac{3}{45}, \quad \frac{1}{9} = \frac{5}{45} \]
- Now, add them:
\[ \text{Combined work rate} = \frac{3}{45} + \frac{5}{45} = \frac{8}{45} \text{ jobs per day} \]

3. **Determine the combined work rate of White, Lee, and Scott:**
- Together, they complete the job in 3 days. Therefore, their combined work rate is:
\[ \text{Combined work rate of White, Lee, and Scott} = \frac{1}{3} \text{ jobs per day} \]

4. **Set up the equation to find Scott's work rate:**
- Let Scott's work rate be \( S \). Then we have:
\[ \frac{8}{45} + S = \frac{1}{3} \]

5. **Solve for Scott's work rate \( S \):**
- First, convert \(\frac{1}{3}\) to a fraction with a denominator of 45:
\[ \frac{1}{3} = \frac{15}{45} \]
- Now, substitute this back into the equation:
\[ \frac{8}{45} + S = \frac{15}{45} \]
- Rearranging gives:
\[ S = \frac{15}{45} - \frac{8}{45} = \frac{7}{45} \text{ jobs per day} \]

6. **Calculate the time taken by Scott to complete the job alone:**
- If Scott's work rate is \(\frac{7}{45}\) jobs per day, then the time taken by Scott to complete 1 job is the reciprocal of his work rate:
\[ \text{Time taken by Scott} = \frac{1}{S} = \frac{1}{\frac{7}{45}} = \frac{45}{7} \text{ days} \]
- Converting this to a mixed fraction:
\[ \frac{45}{7} = 6 \frac{3}{7} \text{ days} \]

### Final Answer:
Scott alone can do the job in \( 6 \frac{3}{7} \) days.