Pipes A and B can fill an empty tank in 9 hours and 12 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 4
The correct answer is Option (4) → 10 hours 15 minutes
Take the capacity as the LCM of 9 and 12, that is 36 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 \(\frac{36}{9}=4\) units and B fills \(\frac{36}{12}=3\) units per hour
One round of 2 hours fills \(4+3=7\) units
4 rounds \(=8\) hours fill \(4\times7=28\) units
9th hour (A): \(28+4=32\) units; 10th hour (B): \(32+3=35\) units
Left \(=36-35=1\) unit; the 11th hour is A's, and A fills 1 unit in \(\frac{1}{4}\) hour \(=15\) minutes
Total time \(=10\) hours \(+\;15\) minutes
The tank is full in 10 hours 15 minutes.