Question

Three water pumps, $P_1$, $P_2$, and $P_3$, operate at constant individual rates to fill a large reservoir. The ratio of the pumping rate of $P_1$ to that of $P_2$ is $3 : 4$, and the ratio of the pumping rate of $P_2$ to that of $P_3$ is $3 : 5$.

At 8:00 AM, all three pumps begin filling an empty reservoir together. At 10:00 AM, pump $P_1$ shuts down, while $P_2$ and $P_3$ continue operating at their original rates. At 11:00 AM, the operating rate of $P_2$ is decreased by $25\%$, and the operating rate of $P_3$ is increased by $25\%$. The two remaining pumps continue at these adjusted rates until the reservoir is completely full at 1:00 PM.

If pump $P_3$ were to fill the empty reservoir working alone at its original constant rate, how many hours would it take?