Thursday, September 30, 2010

Volume P6

Water from 3 taps was used to fill an empty water tank. Tap X, Tap Y, Tap Z could fill the tank completely in 3 hours, 4 hours, 5 hours respectively.
(a) What fraction of the tank was filled with water after half an hour when all taps were turned on at the same time? Give your answer in the simplest form.

Now, only Tap X and Tap Y were both turned on to fill another empty water tank. Immediately after 20 minutes, Tap Z was also turned on. Both Tap X and Tap Y were turned off at the same time after turning on for an hour and only Tap Z was left to fill the tank completely.
(b) How much longer would Tap Z take to fill the tank completely with water after both Tap X and Tap Y were turned off? Express your answer in terms of hours in its simplest form.
(a) 47/120 (b) 1 & 5/12 h


X + Y + Z : 1 h --> 1/3 + 1/4 + 1/5 = 47/60

                   1/2 h --> 1/2 x  4/60 = 47/120

a) It was 47/120.


60 - 20 = 40 min
            = 40/60 h
            = 2/3 h

Z : 1 h --> 1/5

     2/3 h --> 2/3 x 1/5 = 2/15

X + Y : 1 h --> 1/3 + 1/4 = 7/12

2/15 + 7/12 = 43/60

1 - 43/60 = 17/60

60/60 --> 5 h

17/60 --> 17/60 x 5 = 17/12 h
                                    = 1 5/12 h

b) It was 1 5/12 h.

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