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

Answer 1

Answer: (A)

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.

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:
$\frac{x}{2} = \frac{120}{2} = 60 \ \text{minutes} = 1 \ \text{hour}.$