A father can do a job as fast as his two sons working together. If one son does the job in 3 hours and the other in 6 hours, the number of hours taken by the father, to do the job alone is

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem, we need to determine how long it takes for the father to complete a job alone, given that he works as fast as his two sons working together.

### Step-by-Step Solution:

1. **Determine the work rate of each son:**
- The first son can complete the job in 3 hours. Therefore, his work rate is:
\[ \text{Work rate of Son 1} = \frac{1 \text{ job}}{3 \text{ hours}} = \frac{1}{3} \text{ jobs per hour} \]
- The second son can complete the job in 6 hours. Therefore, his work rate is:
\[ \text{Work rate of Son 2} = \frac{1 \text{ job}}{6 \text{ hours}} = \frac{1}{6} \text{ jobs per hour} \]

2. **Calculate the combined work rate of both sons:**
- To find the combined work rate of the two sons, we add their individual work rates:
\[ \text{Combined work rate} = \frac{1}{3} + \frac{1}{6} \]
- To add these fractions, we need a common denominator. The least common multiple of 3 and 6 is 6. Thus:
\[ \frac{1}{3} = \frac{2}{6} \]
- Now we can add:
\[ \text{Combined work rate} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} \text{ jobs per hour} \]

3. **Determine the father's work rate:**
- The father works as fast as both sons together, so his work rate is also:
\[ \text{Father's work rate} = \frac{1}{2} \text{ jobs per hour} \]

4. **Calculate the time taken by the father to complete the job alone:**
- If the father can complete \(\frac{1}{2}\) of a job in one hour, then to complete 1 job, we can use the formula:
\[ \text{Time} = \frac{\text{Total work}}{\text{Work rate}} = \frac{1 \text{ job}}{\frac{1}{2} \text{ jobs per hour}} = 2 \text{ hours} \]

Thus, the father will take **2 hours** to complete the job alone.

### Final Answer:
The number of hours taken by the father to do the job alone is **2 hours**.