Pipes A and B can fill an empty tank in 6 hours and 8 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) → 6 hours 45 minutes
Take the capacity as the LCM of 6 and 8, that is 24 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 \(\frac{24}{6}=4\) units and B fills \(\frac{24}{8}=3\) units per hour
One round of 2 hours fills \(4+3=7\) units
3 rounds \(=6\) hours fill \(3\times7=21\) units
Left \(=24-21=3\) units; the 7th hour is A's, and A fills 3 units in \(\frac{3}{4}\) hour \(=45\) minutes
Total time \(=6\) hours \(+\;45\) minutes