A water treatment facility has three inlet pipes, P, Q, and R, and one outlet drain pipe, S, all connected to the same large storage tank. Pipe P alone can fill the empty tank in 10 hours. Pipe Q alone can fill the empty tank in 15 hours. Pipe R alone can fill the empty tank in 30 hours. The outlet drain, Pipe S, when opened alone on a completely full tank, can empty it entirely in 12 hours.

On a particular day, to test how the system behaves under realistic operating conditions, the facility's operators opened Pipe P, Pipe Q, and the outlet drain Pipe S all together at the same time, starting with a completely empty tank, and let the combined system run without any further changes. The operators are now reviewing the results of this test alongside several other possible pipe combinations, to decide which combination of pipes should be used during future routine operations at the facility.