It is currently 20 Nov 2017, 12:31

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Pumps A, B, and C operate at their respective constant rates. Pumps A

Author Message
TAGS:

### Hide Tags

Manager
Joined: 20 Jan 2017
Posts: 63

Kudos [?]: 7 [0], given: 15

Location: United States (NY)
GMAT 1: 750 Q48 V44
GMAT 2: 610 Q34 V41
Re: Pumps A, B, and C operate at their respective constant rates. Pumps A [#permalink]

### Show Tags

02 Feb 2017, 04:53
1) A&B can do the job in $$\frac{6}{5}$$ of an hour; and their rate when working together is $$\frac{1}{6/5}=\frac{5}{6}$$
A&C can do the job in $$\frac{3}{2}$$ of an hour; and their rate when working together is $$\frac{1}{3/2}=\frac{2}{3}$$
B&C can do the job in 2 hours; and their rate when working together is $$\frac{1}{2}$$
2) If we combine all three rates $$\frac{5}{6}+\frac{2}{3}+\frac{1}{2}=\frac{5}{6}+\frac{4}{6}+\frac{3}{6}=\frac{12}{6}=2$$ (2 tanks in an hour) then we have each machine represented twice. If we divide it by 2 ($$\frac{2}{2}=1$$), then we see that pumps A, B, and C when working together can fill one tank in one hour

Kudos [?]: 7 [0], given: 15

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1819

Kudos [?]: 933 [0], given: 3

Location: United States (CA)
Re: Pumps A, B, and C operate at their respective constant rates. Pumps A [#permalink]

### Show Tags

08 Feb 2017, 11:20
chicagocubsrule wrote:
Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.

A. 1/3
B. 1/2
C. 1/4
D. 1
E. 5/6

We are given that pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours. Recall that rate = work/time. If we consider the work (filling the tank) as 1, then the combined rate of pumps A and B is 1/(6/5). We can express this in the following equation in which a = the time it takes pump A to fill the tank when working alone (thus 1/a is pump A’s rate) and b = the time it takes pump B to fill the tank when working alone (thus 1/b is pump B’s rate):

1/a + 1/b = 1/(6/5)

1/a + 1/b = 5/6

We are next given that pumps A and C, operating simultaneously, can fill the tank in 3/2 hours. We can create another equation in which c = the time it takes pump C to fill the tank alone.

1/a + 1/c = 1/(3/2)

1/a + 1/c = 2/3

Finally, we are given that pumps B and C, operating simultaneously, can fill the tank in 2 hours. We can create the following equation:

1/b + 1/c = ½

Next we can add all three equations together:

(1/a + 1/b = 5/6) + (1/a + 1/c = 2/3) + (1/b + 1/c = ½)

2/a + 2/b + 2/c = 5/6 + 2/3 + 1/2

2/a + 2/b + 2/c = 5/6 + 4/6 + 3/6

2/a + 2/b + 2/c = 12/6

2/a + 2/b + 2/c = 2

Since we need to determine the combined rate of all three machines when filling 1 tank, we can multiply the above equation by ½:

(2/a + 2/b + 2/c = 2) x ½

1/a + 1/b + 1/c = 1

Since the combined rate of all 3 pumps is 1 and time = work/rate, the time needed to fill the tank when all 3 pumps are operating simultaneously is 1/1 = 1 hour.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 933 [0], given: 3

Manager
Joined: 24 Jun 2017
Posts: 110

Kudos [?]: 14 [0], given: 125

Re: Pumps A, B, and C operate at their respective constant rates. Pumps A [#permalink]

### Show Tags

14 Aug 2017, 15:16
corrected myself

a+b=5/6
a+c = 2/3
b+c = 1/2

so resolving by b
b= 1/2 -c
a = 2/3 - c
then first equation a+b=5/6 is

1/2-c+2/3 - c = 5/6
2c + 7/6 = 5/6
2c = 2/6
c= 1/6

then find others by substituting c into the rest equations
a = 1/2 b=1/3 and c=1/6 by summing them we get 1

Kudos [?]: 14 [0], given: 125

Intern
Joined: 21 Sep 2016
Posts: 13

Kudos [?]: 11 [0], given: 81

Location: Zambia
Schools: Duke '20
GMAT 1: 590 Q44 V27
GPA: 3
Re: Pumps A, B, and C operate at their respective constant rates. Pumps A [#permalink]

### Show Tags

25 Aug 2017, 09:44
When you look at the world do you just see one's and zero's 10101011 like the matrix? Solutions are ninja. Took me a while to figure this out.

Bunuel wrote:
chicagocubsrule wrote:
Pumps A, B, and C operate at their respective constant rates. Pumps A & B, operating simultaneously, can fill a certain tank in 6/5 hours; Pumps A & C, operating simultaneously, can fill the tank in 3/2 hours, and pumps B & C, operating simultaneously can fill the tank in 2 hours. How many hours does it take pumps A, B, & C, operating simultaneously, to fill the tank?

a) 1/3
b) 1/2
c) 1/4
d) 1
e) 5/6

A and B = 5/6 --> 1/A+1/B=5/6
A and C = 2/3 --> 1/A+1/C=2/3
B and C = 1/2 --> 1/B+1/C=1/2

Q 1/A+1/B+1/C=?

Add the equations: 1/A+1/B+1/A+1/C+1/B+1/C=5/6+2/3+1/2=2 --> 2*(1/A+1/B+1/A+1/C)=2 --> 1/A+1/B+1/A+1/C=1

Kudos [?]: 11 [0], given: 81

Re: Pumps A, B, and C operate at their respective constant rates. Pumps A   [#permalink] 25 Aug 2017, 09:44

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by