Question

Two pipes A and B together can fill a tank in 40 minutes. Pipe A is twice as fast as pipe B. Pipe A alone can fill the tank in:

• A. 1 hour
• B. 2 hours
• C. 80 minutes
• D. 20 minutes

Hint:

When working with rates of work or filling tasks, the combined rate of two workers (or pipes in this case) is simply the sum of their individual rates. If one pipe is faster than the other, the relationship between their rates can help you set up an equation and solve for unknowns. In this case, using the equation for the combined rate helps determine the time each pipe takes individually.

Answer 1

The Correct Option is A

Let the time taken by pipe \( B \) alone to fill the tank be \( x \) minutes. Since pipe \( A \) is twice as fast as pipe \( B \), the time taken by pipe \( A \) to fill the tank alone is \( \frac{x}{2} \) minutes.

The combined rate of pipes \( A \) and \( B \) is:  
\(\frac{1}{x} + \frac{2}{x} = \frac{3}{x}.\)

The two pipes together can fill the tank in 40 minutes, so their combined rate is:  \(\frac{1}{40}.\)

Equating the rates:  
\(\frac{3}{x} = \frac{1}{40}.\)

Solve for \( x \):  
\(x = 120 \ \text{minutes}.\)

Thus, pipe \( A \) alone can fill the tank in:  
\(\frac{x}{2} = \frac{120}{2} = 60 \ \text{minutes} = 1 \ \text{hour}.\)

Answer 2

Let the time taken by pipe \( B \) alone to fill the tank be \( x \) minutes. Since pipe \( A \) is twice as fast as pipe \( B \), the time taken by pipe \( A \) to fill the tank alone is \( \frac{x}{2} \) minutes.

Step 1: Calculate the combined rate of pipes \( A \) and \( B \):

The rate at which pipe \( B \) fills the tank is \( \frac{1}{x} \) (since it takes \( x \) minutes to fill the tank). The rate at which pipe \( A \) fills the tank is \( \frac{2}{x} \) (since pipe \( A \) is twice as fast as pipe \( B \)). The combined rate of pipes \( A \) and \( B \) is the sum of these rates: \[ \frac{1}{x} + \frac{2}{x} = \frac{3}{x}. \]

Step 2: Set up the equation for the combined rate:

We are told that the two pipes together can fill the tank in 40 minutes, so their combined rate is \( \frac{1}{40} \). Thus, we equate the combined rate of the pipes to \( \frac{1}{40} \): \[ \frac{3}{x} = \frac{1}{40}. \]

Step 3: Solve for \( x \):

Cross-multiply to solve for \( x \): \[ 3 \times 40 = x \implies x = 120. \]

Step 4: Calculate the time taken by pipe \( A \) alone:

The time taken by pipe \( A \) to fill the tank is \( \frac{x}{2} \). Substituting \( x = 120 \): \[ \frac{x}{2} = \frac{120}{2} = 60 \text{ minutes} = 1 \text{ hour}. \]

Conclusion: Pipe \( A \) alone can fill the tank in 60 minutes, or 1 hour.