Question

It takes 6 hours for pump A, used alone, to fill a tank of water. Pump B alone takes 8 hours to fill the same tank. A, B and another pump C all together fill the tank in 2 hours. How long would pump C take, used alone, to fill the tank?

• A. 4.8
• B. 6
• C. 5.6
• D. 3

Answer 1

The Correct Option is A

To solve this problem, we first determine the rates at which pumps A, B, and C fill the tank. The rate of filling is measured in tanks per hour.

1. Pump A, alone, fills the tank in 6 hours. Thus, its rate is \( \frac{1}{6} \) tank per hour. 

2. Pump B, alone, fills the tank in 8 hours. Thus, its rate is \( \frac{1}{8} \) tank per hour.

3. When pumps A, B, and C are used together, they fill the tank in 2 hours. Thus, their combined rate is \( \frac{1}{2} \) tank per hour.

Let's denote the rate of pump C as \( \frac{1}{c} \) tank per hour. The combined rate of the three pumps can be expressed as:

\[\frac{1}{6} + \frac{1}{8} + \frac{1}{c} = \frac{1}{2}\]

We need to find the value of \( c \). First, find a common denominator for the fractions on the left side:

\[\frac{1}{6} = \frac{4}{24}, \frac{1}{8} = \frac{3}{24}\]

So, the equation becomes:

\[\frac{4}{24} + \frac{3}{24} + \frac{1}{c} = \frac{1}{2}\]

Combine the fractions on the left:

\[\frac{7}{24} + \frac{1}{c} = \frac{1}{2}\]

Subtract \( \frac{7}{24} \) from both sides:

\[\frac{1}{c} = \frac{1}{2} - \frac{7}{24}\]

Find a common denominator and subtract the fractions:

\[\frac{1}{2} = \frac{12}{24}, \text{ so } \frac{1}{2} - \frac{7}{24} = \frac{12}{24} - \frac{7}{24} = \frac{5}{24}\]

Thus,

\[\frac{1}{c} = \frac{5}{24}\]

To solve for \( c \), take the reciprocal:

\[c = \frac{24}{5}\]

This gives us \( c = 4.8 \) hours for pump C to fill the tank alone. Therefore, the correct answer is 4.8 hours.