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Answer :
To determine how long it would take the second pump to fill the tank on its own, let's break down the problem step by step:
1. Understand the filling rates:
- The first pump can fill the tank by itself in 150 minutes. This means the first pump fills [tex]\(\frac{1}{150}\)[/tex] of the tank per minute.
- Both pumps together can fill the tank in 60 minutes. So, together, the pumps fill [tex]\(\frac{1}{60}\)[/tex] of the tank per minute.
2. Set up the equation:
- We are looking for the time it takes for the second pump alone to fill the tank, which we'll call [tex]\(x\)[/tex]. Thus, the second pump alone fills [tex]\(\frac{1}{x}\)[/tex] of the tank per minute.
- The equation for the rates of the two pumps working together is:
[tex]\[
\frac{1}{150} + \frac{1}{x} = \frac{1}{60}
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
- Rearrange the equation to solve for [tex]\(\frac{1}{x}\)[/tex]:
[tex]\[
\frac{1}{x} = \frac{1}{60} - \frac{1}{150}
\][/tex]
- Calculate the right hand side:
[tex]\[
\frac{1}{60} = \frac{5}{300}, \quad \frac{1}{150} = \frac{2}{300}
\][/tex]
[tex]\[
\frac{1}{x} = \frac{5}{300} - \frac{2}{300} = \frac{3}{300} = \frac{1}{100}
\][/tex]
- From this, we find:
[tex]\[
x = 100
\][/tex]
Thus, the second pump, when working alone, would take 100 minutes to fill the tank. The correct answer is C. 100 minutes.
1. Understand the filling rates:
- The first pump can fill the tank by itself in 150 minutes. This means the first pump fills [tex]\(\frac{1}{150}\)[/tex] of the tank per minute.
- Both pumps together can fill the tank in 60 minutes. So, together, the pumps fill [tex]\(\frac{1}{60}\)[/tex] of the tank per minute.
2. Set up the equation:
- We are looking for the time it takes for the second pump alone to fill the tank, which we'll call [tex]\(x\)[/tex]. Thus, the second pump alone fills [tex]\(\frac{1}{x}\)[/tex] of the tank per minute.
- The equation for the rates of the two pumps working together is:
[tex]\[
\frac{1}{150} + \frac{1}{x} = \frac{1}{60}
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
- Rearrange the equation to solve for [tex]\(\frac{1}{x}\)[/tex]:
[tex]\[
\frac{1}{x} = \frac{1}{60} - \frac{1}{150}
\][/tex]
- Calculate the right hand side:
[tex]\[
\frac{1}{60} = \frac{5}{300}, \quad \frac{1}{150} = \frac{2}{300}
\][/tex]
[tex]\[
\frac{1}{x} = \frac{5}{300} - \frac{2}{300} = \frac{3}{300} = \frac{1}{100}
\][/tex]
- From this, we find:
[tex]\[
x = 100
\][/tex]
Thus, the second pump, when working alone, would take 100 minutes to fill the tank. The correct answer is C. 100 minutes.
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