Question

It takes 6 hours for pump A, used alone, to fill a tank of water. Pump B used 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

Hint:

Add the rates of A, B and C to equal the combined rate of 1/2 tank per hour, then solve for C's rate.

Answer 1

The Correct Option is A

Step 1: Write the individual rates of A and B.
Pump A fills the tank in 6 hours, so its rate is \(\frac{1}{6}\) tank per hour. Pump B fills the tank in 8 hours, so its rate is \(\frac{1}{8}\) tank per hour.
Step 2: Write the combined rate of A, B and C.
Together they fill the tank in 2 hours, so their combined rate is \(\frac{1}{2}\) tank per hour.
Step 3: Find the rate of pump C alone.
Rate of C = combined rate - rate of A - rate of B \(= \frac{1}{2} - \frac{1}{6} - \frac{1}{8}\). Taking the LCM of 2, 6 and 8, which is 24: \(\frac{12}{24} - \frac{4}{24} - \frac{3}{24} = \frac{5}{24}\) tank per hour.
Step 4: Convert the rate of C into time.
Time taken by C alone = reciprocal of its rate \(= \frac{24}{5} = 4.8\) hours.
Step 5: Rule out the other options.
Option 2 (6 hours) would mean C's rate is \(\frac{1}{6}\), which does not satisfy the combined rate equation. Options 3 (5.6) and 4 (3) also fail when checked back into the equation. Only 4.8 hours satisfies all the given conditions.