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13 Jul 2018, 00:47
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D
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Difficulty:
5%
(low)
Question Stats:
89% (01:20) correct
11%
(01:56)
wrong
based on 175
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Date
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Three pumps, P, R, and T, working simultaneously at their respective constant rates, can fill a tank in 5 hours. Pumps P and R, working simultaneously at their respective constant rates, can fill the tank in 7 hours. How many hours will it take pump T, working alone at its constant rate, to fill the tank?
A) 1.7
B) 10.0
C) 15.0
D) 17.5
E) 30.0
A) 1.7
B) 10.0
C) 15.0
D) 17.5
E) 30.0
13 Jul 2018, 01:56
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+1 for D.
Pumps P and R can fill 1/7 of the tank in 1 hour
Pumps P, R, and T can fill 1/5 of the tank in 1 hour
So, working alone Pump T can fill :
1/5 - 1/7
(7 - 5)/35
2/35 of the tank in 1 hour
Therefore, working alone Pump T can fill the tank in 35/2, i.e,17.5 hours.
Hence, D.
Pumps P and R can fill 1/7 of the tank in 1 hour
Pumps P, R, and T can fill 1/5 of the tank in 1 hour
So, working alone Pump T can fill :
1/5 - 1/7
(7 - 5)/35
2/35 of the tank in 1 hour
Therefore, working alone Pump T can fill the tank in 35/2, i.e,17.5 hours.
Hence, D.
13 Jul 2018, 04:08
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We can use the "magic formula" for this one.
P, R and T working together can do the job in 5 hours: \(\frac{1}{P} + \frac{1}{R} + \frac{1}{T} = \frac{1}{5}\)
P and R working together can do the job in 7 hours: \(\frac{1}{P} + \frac{1}{R} = \frac{1}{7}\)
We can replace \(\frac{1}{P} + \frac{1}{R}\) by \(\frac{1}{7}\)
This results in: \(\frac{1}{7}+ \frac{1}{T} = \frac{1}{5}\)
We can now find T = 35/2 = 17.5 hours
Answer D.
P, R and T working together can do the job in 5 hours: \(\frac{1}{P} + \frac{1}{R} + \frac{1}{T} = \frac{1}{5}\)
P and R working together can do the job in 7 hours: \(\frac{1}{P} + \frac{1}{R} = \frac{1}{7}\)
We can replace \(\frac{1}{P} + \frac{1}{R}\) by \(\frac{1}{7}\)
This results in: \(\frac{1}{7}+ \frac{1}{T} = \frac{1}{5}\)
We can now find T = 35/2 = 17.5 hours
Answer D.
