Pipes A and B can fill an empty tank in 9 hours and 6 hours respectively. The tank is empty. The pipes are opened one at a time, for 1 hour each, in the order A, B, A, B, and so on, starting with A. In how much time will the tank be full?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7 hours 20 minutes
Take the capacity as the LCM of 9 and 6, that is 18 units. Count the filling in rounds of 2 hours (one hour of A, then one hour of B), and finish the last part hour by hour.
A fills \(\frac{18}{9}=2\) units and B fills \(\frac{18}{6}=3\) units per hour
One round of 2 hours fills \(2+3=5\) units
3 rounds \(=6\) hours fill \(3\times5=15\) units
7th hour (A): \(15+2=17\) units; left \(=1\) unit
The 8th hour is B's, and B fills 1 unit in \(\frac{1}{3}\) hour \(=20\) minutes
Total time \(=7\) hours \(+\;20\) minutes