Could anyone help me with this problem please?

Archimedes has a bath which is filled using three taps labelled A, B and C.

The rates of flow of B is twice that of A, the rates of flow of C is three times that of A.

Yesterday, Archimedes filled his bath as follows:

Firstly he used all three taps for 2 hours. Then he turned off B and finished filling the bath in an additional 2 hours and 45 mins using taps A and C only (it's a very big bath).

Today Archimedes is going to fill his bath (currently empty) using all three taps.

How long will this take him?