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

Given that two pipes A and B together can fill a tank in 40 minutes and pipe A is twice as fast as pipe B, we need to find out how long pipe A alone can fill the tank. 

Let's assume the rate at which pipe B fills the tank is \(x\) tanks per minute. Then, the rate at which pipe A fills the tank is \(2x\) tanks per minute because pipe A is twice as fast as pipe B.

Using the information that pipes A and B together can fill the tank in 40 minutes, we express their combined rate of filling tanks as \(x + 2x = 3x\).

The combined rate of 3x pipes per minute is enough to fill 1 tank in 40 minutes, so we have:

\[ 3x \times 40 = 1 \]

Solving for x:

\[ 3x = \frac{1}{40} \]

\[ x = \frac{1}{120} \]

Now that we know the rate for pipe B (x), let's use it to find the rate for pipe A, which is \(2x = 2 \times \frac{1}{120} = \frac{1}{60}\).

This means pipe A alone can fill the tank at a rate of \(\frac{1}{60}\) tanks per minute, translating to filling the entire tank in 60 minutes or 1 hour.

Therefore, the correct answer is: 1 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.