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A tank has two inlet taps P and Q and an outlet tap R. When empty, the tank can be filled by tap P alone in #4 1/2# hours or by tap Q alone in 3 hours. When full, the tank can be emptied in 2 hours by tap R.
(a) The tank is initially empty. Find how long it would take to fill up the tank: (i) If tap R is closed and taps P and Q are opened at the same time.
(ii) If all the three taps are opened at the same time.
(b) The tank is initially empty and the three taps are opened as follows: P at 8.00 am Q at 8.45 am R at 9.00 am
(i) Find the fraction of the tank that would be filled by 9.00 a.m. (ii) Find the time the tank would be fully filled up.