Tap K can fill a tank in 8 hours and tap L can fill the same tank in 20 hours. In how many hours both tap K and L together can fill the same tank?

Options

A. `20//3` hours
B. `60//11` hours
C. `18//5` hours
D. `40//7` hours

Answer

To solve the problem of how long it takes for taps K and L to fill a tank together, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the filling rates of each tap**:
- Tap K can fill the tank in 8 hours. Therefore, its rate of work is:
\[ \text{Rate of K} = \frac{1 \text{ tank}}{8 \text{ hours}} = \frac{1}{8} \text{ tanks per hour} \]
- Tap L can fill the tank in 20 hours. Therefore, its rate of work is:
\[ \text{Rate of L} = \frac{1 \text{ tank}}{20 \text{ hours}} = \frac{1}{20} \text{ tanks per hour} \]

2. **Combine the rates of both taps**:
- When both taps are working together, their combined rate is the sum of their individual rates:
\[ \text{Combined Rate} = \text{Rate of K} + \text{Rate of L} = \frac{1}{8} + \frac{1}{20} \]

3. **Find a common denominator to add the fractions**:
- The least common multiple (LCM) of 8 and 20 is 40. We can convert both fractions:
\[ \frac{1}{8} = \frac{5}{40} \quad \text{and} \quad \frac{1}{20} = \frac{2}{40} \]
- Now, add the two rates:
\[ \text{Combined Rate} = \frac{5}{40} + \frac{2}{40} = \frac{7}{40} \text{ tanks per hour} \]

4. **Calculate the time taken to fill the tank together**:
- To find the time taken to fill one tank, we take the reciprocal of the combined rate:
\[ \text{Time} = \frac{1 \text{ tank}}{\frac{7}{40} \text{ tanks per hour}} = \frac{40}{7} \text{ hours} \]

### Final Answer:
Thus, the time taken by taps K and L together to fill the tank is:
\[ \frac{40}{7} \text{ hours} \]