Question 1149845
a tank has 2 inlets P and Q and an outlet tap R .

when empty the tank can be filled by tap P alone in 4 and a half hours 
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So tap P's filling rate is 1 tank per 4 1/2 hours or
1 tank per 9/2 hours or 1/(9/2) tank per hour or 2/9 tank per hour
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or by tap Q alone in 3 hours. 
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So tap P's filling rate is 1 tank per 3 hours or 1/3 tank per hour
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when full the tank can be emptied in 2 hours by tap R
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So tap R's emptying rate (negative filling rate) is -1 tank per 2 hours or
-1/2 tank per hour
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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.
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Their combined rate is 2/9 + 1/3 = 2/9  + 3/9 = 5/9 tank/hour

In x hours they will fill 1 tank:

(5/9)x = 1
     x = 9/5 = 1.8 hours = 1 hour and 48 minutes.
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ii) if all the three taps are opened at the same time.
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Their combined rate is 2/9 + 1/3 - 1/2 = 4/18  + 6/18 - 9/18 = 1/9 tank/hour

In x hours they will fill 1 tank:

(1/9)x = 1
     x = 9 hours.
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B) the tank is initially empty and the three taps are opened as follows:
P at 8:00 A.m    Q at 8.45 A.m   R at 9.00 A.m   

i)find the fraction of the tank that would be filled by 9.00 a.m   
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P has been open 1 hour at 9AM and since it fills 2/9 tank per hour it
has filled 2/9 of the tank.
Q has been open 15 minutes or 1/4 hour at 9AM and since it fills 1/3 of
a tank per hour it has filled 1/4 of 1/3 or 1/12 tank.
R hasn't opend yet, so the fraction of a tank that has been filled is
2/9 + 1/12 = 8/36 + 3/36 = 11/36 of a tank.
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ii)find the time the tank would be fully filled up.
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It is 11/36 full at 9AM so it has 25/36 tank more to go, so in x hours after
9AM it will fill the remaining 25/36 tank at the combined rate of 1/9 tank
per hour, so

(1/9)x = 25/36
     x = (25/36)(9/1) = 25/4 = 6 1/4 hours

6 hours 15 minutes after 9AM is 6:15PM.

Edwin</pre>