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Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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Difficulty:   5% (low)

Question Stats: 90% (01:17) correct 10% (01:55) wrong based on 201 sessions

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Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?

A. 72
B. 75
C. 84
D. 96
E. 108

Kudos for a correct solution.

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Manager  Joined: 21 Aug 2014
Posts: 152
Location: United States
Concentration: Other, Operations
GMAT 1: 700 Q47 V40 GMAT 2: 690 Q44 V40 WE: Science (Pharmaceuticals and Biotech)
Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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Pump A can empty the pool in 3 hours therefore the rate at which it empties is 1/3 pool/hour
Pump b can empty the pool in 2 hours therefore the rate at which it empties is 1/2 pool/hour.

If they work together, the resulting rate is the addition of both rates (1/3 +1/2)pool/hour = 5/6 pool/hour

Now we have the following:

(5/6pool)/60min = 1pool/x

x = 72minutes

Director  Joined: 07 Aug 2011
Posts: 502
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27 Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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Bunuel wrote:
Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?

A. 72
B. 75
C. 84
D. 96
E. 108

Kudos for a correct solution.

Speed of B is 1.5 times of A .
combined speed B+A = 1.5A + A = $$\frac{5}{2}$$ A . so if ideally A takes 3 hrs , with $$\frac{5}{2}$$ *A speed it will take --> $$\frac{3*2}{5}* 60$$ = 72 minutes.

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Posts: 18
Location: Italy
GMAT 1: 670 Q48 V34 GPA: 3.7
Re: Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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Rate of A: $$\frac{1}{3h}$$
Rate of B: $$\frac{1}{2h}$$
Combined rate: $$\frac{1}{3h}+\frac{1}{2h}=\frac{5}{6h}=\frac{5}{360 minutes}=\frac{1}{72 minutes}$$

Answer A is correct
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Re: Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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Answer = A = 72

Rate of pump A $$= \frac{1}{180}$$

Rate of pump B = $$\frac{1}{120}$$

Combined rate $$= \frac{5}{360}$$

Time required for combined work $$= \frac{360}{5} = 72$$
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Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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Bunuel wrote:
Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?

A. 72
B. 75
C. 84
D. 96
E. 108

Kudos for a correct solution.

Let the total work be 1
Rate of work A = Total work done/ Total time taken = 1/3
Rate of work B = Total work done/ Total time taken = 1/2

Total Rate $$= 1/2 + 1/3 = 5/6$$
In 1 hour work done is = 5/6
Time taken to complete the entire work (1) = 6/5 hours

$$(6/5)*60 = 72$$ minutes.

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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1
Hi All,

In this prompt, we have two 'entities' sharing a task (with no *twists*), so the Work Formula will be perfect for this question.

Work = (A)(B)/(A+B) where A and B are the rates of the two entities.

We're given the respective rates for two pumps to empty a pool:

Pump A can empty the pool in 3 hours.
Pump B can empty the pool in 2 hours.

We're asked how long it takes the two pumps, working together, to empty the pool.

Plugging in the respective numbers (the 3 and the 2), we have...

(3)(2)/(3+2) = 6/5 = 1.2 hours = 1 hour 12 minutes

The question asks for an answer in MINUTES. 1 hour 12 minutes = 72 minutes.

GMAT assassins aren't born, they're made,
Rich
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Intern  Joined: 02 Jan 2014
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Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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Combined rate is 1/3+1/2 is 5/6.

time taken to empty pool is 6/5*60 = 72 Mins
Manager  B
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Posts: 52
Re: Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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Total Work Done in 1 hr = (1/2) +(1/3)

Total time in minutes = 6/5 *60 = 72 minutes

Ans : A
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Joined: 21 May 2013
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Re: Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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Bunuel wrote:
Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?

A. 72
B. 75
C. 84
D. 96
E. 108

Kudos for a correct solution.

+1 for A
IN 1 hour, Pump A can empty=1/3 of the pool
In 1 hour, Pump B can empty=1/2 of the pool
Working together, in 1 hour, they can empty=1/3+1/2=5/6 of the pool
Therefore, to empty the pool. both will take=6/5 Hours=6/5*60 minutes=72
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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Bunuel wrote:
Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?

A. 72
B. 75
C. 84
D. 96
E. 108

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment: pumpsaandb_text.PNG [ 17.61 KiB | Viewed 15031 times ]

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Re: Working alone, pump A can empty a pool in 3 hours. Working alone, pump  [#permalink]

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Bunuel wrote:
Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?

A. 72
B. 75
C. 84
D. 96
E. 108

The combined rate of pumps A and B is:

1/3 + 1/2 = 2/6 + 3/6 = 5/6, so the time is 1/(5/6) = 6/5 hours, which is 6/5 x 60 = 72 minutes.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: Working alone, pump A can empty a pool in 3 hours. Working alone, pump   [#permalink] 13 Oct 2018, 18:25
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