Question

A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

• A. 35 hr
• B. 25 hr
• C. 20 hr
• D. 45 hr

Hint:

When solving problems involving multiple contributors with different rates, first find their combined rate to determine the total effort required for the task.

Answer 1

The Correct Option is D

Step 1: Establish the rate relationship between the pipes.
Given the rates of B and C relative to A: \[ \text{Let } A = x, \quad B = 2x, \quad C = 4x \text{ (since C is twice as fast as B and B is twice as fast as A)} \]

Step 2: Calculate the combined rate of A, B, and C.
\[ \text{Combined rate} = x + 2x + 4x = 7x \]

Step 3: Solve for the time it takes A alone to fill the tank.
The combined effort fills the tank in 5 hours, so: \[ 7x \times 5 = 1 \text{ full tank} \] \[ x \times t = 1 \text{ full tank} \quad \text{(for pipe A alone)} \] Since \( 7x = \frac{1}{5} \), then \( x = \frac{1}{35} \) and: \[ t = \frac{1}{x} = 45 \text{ hours} \]