Question

A swimming pool can be filled by pipe A in 3 hours and by pipe B in 6 hours, each pump working on its own. At 9 am, pump A is started. At what time will the swimming pool be filled if pump B is started at 10 am?

• A. 11:20 a.m.
• B. 11:05 a.m.
• C. 11:10 a.m.
• D. 10:50 a.m.

Hint:

Find how much of the pool pipe A fills alone in the first hour, then use the combined rate for the remaining part.

Answer 1

The Correct Option is A

Step 1: Write the rates of pipe A and pipe B.
Pipe A fills the pool in 3 hours, so its rate is \(\frac{1}{3}\) pool per hour. Pipe B fills the pool in 6 hours, so its rate is \(\frac{1}{6}\) pool per hour.
Step 2: Find how much pipe A fills before pipe B joins.
Pipe A runs alone from 9 am to 10 am, which is 1 hour. In this hour it fills \(\frac{1}{3} \times 1 = \frac{1}{3}\) of the pool.
Step 3: Find the remaining part of the pool.
Remaining part \(= 1 - \frac{1}{3} = \frac{2}{3}\) of the pool.
Step 4: Find the combined rate once both pipes are running.
From 10 am onward, both A and B work together, so their combined rate is \(\frac{1}{3} + \frac{1}{6} = \frac{1}{2}\) pool per hour.
Step 5: Find the time needed to fill the remaining part.
Time \(= \frac{2/3}{1/2} = \frac{4}{3}\) hours \(= 1\) hour 20 minutes.
Step 6: Add this time to 10 am.
The pool gets completely filled at \(10{:}00 + 1{:}20 = 11{:}20\) am.
Step 7: Rule out the other options.
Options 2, 3 and 4 do not match the exact 1 hour 20 minute duration calculated from the combined rate, so they are incorrect. Only 11:20 am is correct.