Question

Two identical pumps fill up a water reservoir in 10 hours. How many additional pumps should be turned on if the reservoir must be filled up in 4 hours?

Answer 1

To determine how many additional pumps are needed to fill the reservoir in 4 hours, let's first understand the situation with the given pumps.

1. **Calculating the filling rate of the pumps:**
- Two identical pumps can fill the reservoir in 10 hours. Therefore, their combined rate of filling the reservoir is:
\[
\text{Rate of 2 pumps} = \frac{1 \text{ reservoir}}{10 \text{ hours}} = 0.1 \text{ reservoirs per hour}
\]
- Thus, the rate of one pump is:
\[
\text{Rate of 1 pump} = \frac{0.1 \text{ reservoirs per hour}}{2} = 0.05 \text{ reservoirs per hour}
\]

2. **Calculating the desired rate to fill the reservoir in 4 hours:**
- We need to fill the reservoir in 4 hours, so the required rate of filling is:
\[
\text{Required rate} = \frac{1 \text{ reservoir}}{4 \text{ hours}} = 0.25 \text{ reservoirs per hour}
\]

3. **Determining how many pumps are needed:**
- Let \( n \) be the total number of pumps required to achieve the desired rate of 0.25 reservoirs per hour. The total rate with \( n \) pumps can be expressed as:
\[
\text{Total rate with n pumps} = n \times 0.05 \text{ reservoirs per hour}
\]
- We set this equal to the required rate:
\[
n \times 0.05 = 0.25
\]
- Solving for \( n \):
\[
n = \frac{0.25}{0.05} = 5
\]

4. **Calculating additional pumps needed:**
- Initially, there are 2 pumps. Thus, the number of additional pumps needed is:
\[
\text{Additional pumps} = n - 2 = 5 - 2 = 3
\]

Thus, **3 additional pumps should be turned on** to fill the reservoir in 4 hours.