Question

Pipe A can fill 3 tanks in 10 minutes. Pipe B can fill 5 tanks in 15 minutes. How long will it take for them to fill a single tank if they work together?
30/19 minutes
5/3 minutes
10/19 minutes
10/9 minutes

Answer 1

To determine how long it will take for Pipes A and B to fill a single tank when they work together, we first need to calculate their filling rates.

**Step 1: Calculate the filling rate of each pipe.**

**Pipe A:**
- It can fill 3 tanks in 10 minutes.
- Filling rate of Pipe A = Number of tanks / Time taken = \( \frac{3 \text{ tanks}}{10 \text{ minutes}} = \frac{3}{10} \text{ tanks/minute} \)

**Pipe B:**
- It can fill 5 tanks in 15 minutes.
- Filling rate of Pipe B = Number of tanks / Time taken = \( \frac{5 \text{ tanks}}{15 \text{ minutes}} = \frac{1}{3} \text{ tanks/minute} \)

**Step 2: Add the rates of Pipes A and B.**
\[
\text{Combined filling rate} = \left(\frac{3}{10} + \frac{1}{3}\right) \text{ tanks/minute}
\]

To add these rates, we need a common denominator. The least common multiple of 10 and 3 is 30.

**Converting the rates:**
\[
\frac{3}{10} = \frac{9}{30}
\]
\[
\frac{1}{3} = \frac{10}{30}
\]

So,
\[
\text{Combined filling rate} = \frac{9}{30} + \frac{10}{30} = \frac{19}{30} \text{ tanks/minute}
\]

**Step 3: Calculate the time to fill one tank.**

If they work together to fill 1 tank at a rate of \( \frac{19}{30} \text{ tanks/minute} \), the time \( t \) to fill 1 tank can be calculated as follows:
\[
t = \frac{1 \text{ tank}}{\frac{19}{30} \text{ tanks/minute}} = \frac{30}{19} \text{ minutes}
\]

Therefore, the time taken for Pipes A and B to fill a single tank working together is:

\[
\boxed{\frac{30}{19} \text{ minutes}}
\]