LUANDATO wrote:Consider 20 identical pipes that supply water to a tank. What is the minimum number of pipes that has to be kept open if one needs to fill the tank within 30 minutes?
1) When 8 pipes are kept open, the tank gets filled 20 minutes sooner than when 6 pipes are kept open.
2) If all the 20 pipes are kept open, the tank gets filled in less than 15 minutes.
Statement 1:
Let the rate for each pipe = 1 gallon per minute.
8 pipes:
Since the rate for each pipe = 1 gallon per minute, the rate for 8 pipes = 8 gallons per minute.
Let the time to fill the tank = t.
Since work = (rate)(time), the volume of the tank = rt =
8t.
6 pipes:
Since the rate for each pipe = 1 gallon per minute, the rate for 6 pipes = 6 gallons per minute.
Since 6 pipes take 20 minutes longer than 8 pipes -- and 8 pipes take t minutes to fill the tank -- the time for 6 pipes = t+20.
Since work = (rate)(time), the volume of the tank = rt = (6)(t+20) =
6t+120.
Since the volume of the tank is the same in each case, the expressions in blue must be EQUAL:
8t = 6t+120
2t = 120
t = 60.
Thus:
Volume of the pool = 8t = 8*60 = 480 gallons.
To fill the 480-gallon tank in 30 minutes, the required rate = 480/30 = 16 gallons per minute.
Since the rate for each pipe is 1 gallon per minute -- and the required rate is 16 gallons per minute -- the number of pipes that must be open = 16.
SUFFICIENT.
Statement 2:
Since the time for 20 pipes can be any value less than 15, there is no way to determine a rate for each pipe and thus no way to determine the minimum number required to fill the tank in 30 minutes.
INSUFFICIENT.
The correct answer is
A.
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