A can do a piece of work in 14 days while B can do it in 28 days. In how many days, working together will they complete the whole work?

Options

A. 10.5
B. 8
C. `28/3`
D. 9

Answer

To solve the problem of how many days A and B will take to complete the work together, we can follow these steps:

### Step 1: Determine the work done by A and B individually.
- A can complete the work in 14 days.
- B can complete the work in 28 days.

### Step 2: Calculate the work done by A in one day.
- Since A completes the work in 14 days, the work done by A in one day is:
\[ \text{Work done by A in one day} = \frac{1}{14} \text{ of the work} \]

### Step 3: Calculate the work done by B in one day.
- Since B completes the work in 28 days, the work done by B in one day is:
\[ \text{Work done by B in one day} = \frac{1}{28} \text{ of the work} \]

### Step 4: Find the combined work done by A and B in one day.
- To find the total work done by A and B together in one day, we add their individual work rates:
\[ \text{Combined work in one day} = \frac{1}{14} + \frac{1}{28} \]

### Step 5: Calculate the combined work rate.
- To add the fractions, we need a common denominator. The least common multiple of 14 and 28 is 28:
\[ \frac{1}{14} = \frac{2}{28} \]
- Now we can add:
\[ \text{Combined work in one day} = \frac{2}{28} + \frac{1}{28} = \frac{3}{28} \]

### Step 6: Calculate the total time taken to complete the work together.
- If A and B together can complete \(\frac{3}{28}\) of the work in one day, then the total time taken to complete the whole work is the reciprocal of the combined work rate:
\[ \text{Total time} = \frac{1}{\frac{3}{28}} = \frac{28}{3} \text{ days} \]

### Final Answer:
- Therefore, A and B together will complete the work in \(\frac{28}{3}\) days.

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