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# Three pumps, P, R, and T, working simultaneously at their respective

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Math Expert
Joined: 02 Sep 2009
Posts: 52902
Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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12 Jul 2018, 23:47
00:00

Difficulty:

5% (low)

Question Stats:

90% (01:19) correct 10% (01:35) wrong based on 75 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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Re: Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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13 Jul 2018, 00:56
+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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Joined: 17 May 2018
Posts: 44
Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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13 Jul 2018, 03:08
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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Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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13 Jul 2018, 06:17
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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Re: Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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13 Jul 2018, 06:23
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
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Three pumps, P, R, and T, working simultaneously at their respective  [#permalink]

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02 Oct 2018, 05:21
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, 05:21
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