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Math Expert V
Joined: 02 Sep 2009
Posts: 58464
Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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Difficulty:   5% (low)

Question Stats: 90% (01:19) correct 10% (01:35) wrong based on 76 sessions

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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

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Retired Moderator D
Joined: 30 Jan 2015
Posts: 794
Location: India
Concentration: Operations, Marketing
GPA: 3.5
Re: Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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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.
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Thanks Intern  B
Joined: 17 May 2018
Posts: 48
Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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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

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Senior Manager  G
Joined: 04 Aug 2010
Posts: 477
Schools: Dartmouth College
Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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Bunuel wrote:
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

Let the tank = the LCM of the two times = 35 liters.
Since P+R+T take 5 hours to fill the 35-liter tank, the rate for $$P+R+T = \frac{35}{5} = 7$$ liters per hour.
Since P+R take 7 hours to fill the 35-liter tank, the rate for $$P+R = \frac{35}{7} = 5$$ liters per hour.
P's rate = (rate for P+R+T) - (rate for P+R) = 7-5 = 2 liters per hour.
Since P's rate = 2 liters per hour, the time for P to fill the 35-liter tank $$=\frac{35}{2} = 17.5$$ hours.

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Manager  G
Joined: 14 Jun 2018
Posts: 215
Re: Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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P , R ,T does 100% work in 5 hour. Therefore , 20% in 1 hour
P, R does 100% work in 7 hour. Therefore , 14.28% in 1 hour
20 - 14.28 = 5.72% work is done by T in 1 hour.
T does 100% in (100/5.72) hours = 17.5 hour
Intern  B
Joined: 16 May 2017
Posts: 48
GPA: 3.8
WE: Medicine and Health (Health Care)
Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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Work done by P,R,T in an hour=1/5
Work done by P,R in an hour=1/7
Work done by T in an hour=1/5-1/7=2/35

So, time taken by T=35/2= 17.5 hrs

(D) Three pumps, P, R, and T, working simultaneously at their respective   [#permalink] 02 Oct 2018, 06:21
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