Question

Pipe A can fill 3 tanks in 8 minutes. Pipe B can fill 5 tanks in 10 minutes. How long will it take for them to fill a single tank if they work together?
10/9 minutes
8/7 minutes
7/8 minutes
8/5 minutes

Answer 1

To find out how long it will take for both Pipe A and Pipe B to fill a single tank when working together, we first calculate the filling rates of each pipe.

1. **Calculate the rate of Pipe A**:
- Pipe A fills 3 tanks in 8 minutes.
- The rate of Pipe A = \(\frac{3 \text{ tanks}}{8 \text{ minutes}} = \frac{3}{8} \text{ tanks per minute}\).

2. **Calculate the rate of Pipe B**:
- Pipe B fills 5 tanks in 10 minutes.
- The rate of Pipe B = \(\frac{5 \text{ tanks}}{10 \text{ minutes}} = \frac{1}{2} \text{ tanks per minute}\).

3. **Combine the rates of both pipes**:
- The combined rate when both pipes work together = Rate of Pipe A + Rate of Pipe B
- Combined rate = \(\frac{3}{8} + \frac{1}{2}\).

To add these fractions, we need a common denominator. The least common multiple of 8 and 2 is 8.

- The fraction \(\frac{1}{2}\) can be rewritten as \(\frac{4}{8}\).

Now we can add:
\[
\frac{3}{8} + \frac{4}{8} = \frac{7}{8} \text{ tanks per minute}.
\]

4. **Calculate the time to fill 1 tank**:
- Time = \(\frac{\text{Amount of tanks}}{\text{Rate}}\).
- Here, we want to fill 1 tank, so:
\[
\text{Time} = \frac{1 \text{ tank}}{\frac{7}{8} \text{ tanks per minute}} = \frac{1}{\frac{7}{8}} = \frac{8}{7} \text{ minutes}.
\]

Therefore, the time it will take for both pipes to fill one tank if they work together is \(\frac{8}{7}\) minutes.

The correct answer is **8/7 minutes**.