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# Pump A can empty a pool in A minutes, and pump B can empty

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Director
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Pump A can empty a pool in A minutes, and pump B can empty [#permalink]  07 Oct 2017, 02:02
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Question Stats:

50% (01:33) correct 50% (00:51) wrong based on 6 sessions
Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?

A) $$\frac{A+B-1}{2}$$

B) $$\frac{A(B+1)}{A+B}$$

C) $$\frac{AB}{A+B}$$

D) $$\frac{A+B}{A+B}-1$$

E) $$\frac{A(B-1)}{A+B}$$

This question is from Magoosh weekly practice questions. I already saw their explanation but I am looking for some other ways to do it if there exists. So, please don't Google it and try to develop the answer by your own.
[Reveal] Spoiler: OA
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Joined: 18 Apr 2015
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Kudos [?]: 1119 [0], given: 5180

Re: Pump A can empty a pool in A minutes, and pump B can empty [#permalink]  07 Oct 2017, 02:19
Expert's post
This is a GMAT one or GRE ?? well, most of the notions overlap.

https://gmatclub.com/forum/pump-a-can-e ... 66579.html

Intuitively, the rate combined of two types of machinery is in general $$\frac{A*B}{A+B}$$.

Add 1 to B because of it starts later on.

B

Regards

PS: do not forget the level of difficulty tab.
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Director
Joined: 03 Sep 2017
Posts: 521
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Kudos [?]: 343 [1] , given: 66

Re: Pump A can empty a pool in A minutes, and pump B can empty [#permalink]  07 Oct 2017, 02:35
1
KUDOS
Carcass wrote:
This is a GMAT one or GRE ?? well, most of the notions overlap.

https://gmatclub.com/forum/pump-a-can-e ... 66579.html

Intuitively, the rate combined of two types of machinery is in general $$\frac{A*B}{A+B}$$.

Add 1 to B because of it starts later on.

B

Regards

PS: do not forget the level of difficulty tab.

On Magoosh is among the GRE ones, but it's true there are many questions overlapping.

Moving to the answer: how do you justify 1 is not only added but also multiplied by A?
Moderator
Joined: 18 Apr 2015
Posts: 5600
Followers: 89

Kudos [?]: 1119 [0], given: 5180

Re: Pump A can empty a pool in A minutes, and pump B can empty [#permalink]  07 Oct 2017, 02:59
Expert's post
Because after years of this tests I developed an instinct.

C is the standard formula for the work combined. Out. The pumps are not aligned

E has no sense because B has to catch up A not the other way around

D has no sense the - 1 at post of the fraction

A We do know that the numerator must be a multiplication, not a sum.

B is left.

These are sorts of a thing you have after years. You suddenly know what is wrong. It is something in your mind. 8000 kudos on gmatclub and now here since 2 years......well, they need for something
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Kudos [?]: 120 [1] , given: 0

Re: Pump A can empty a pool in A minutes, and pump B can empty [#permalink]  02 Jan 2018, 08:48
1
KUDOS
Expert's post
IlCreatore wrote:
Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?

A) $$\frac{A+B-1}{2}$$

B) $$\frac{A(B+1)}{A+B}$$

C) $$\frac{AB}{A+B}$$

D) $$\frac{A+B}{A+B}-1$$

E) $$\frac{A(B-1)}{A+B}$$

We can let the rate of pump A = 1/A and the rate of pump B = 1/B.

We can let the time of pump A = T and the time of pump B = T - 1.

We will use the equation for work to answer the question: work = rate x time. We sum the individual work of pumps A and B, and they perform 1 job, which is to empty the entire pool. Thus, we create the following equation:

(1/A)(T) + (1/B)(T - 1) = 1

T/A + (T - 1)/B = 1

Multiplying by AB, we have:

TB + TA - A = AB

TB + TA = AB + A

T(B + A) = AB + A

T = (AB + A)/(B + A)

T = A(B + 1)/(B + A)

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Director
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Re: Pump A can empty a pool in A minutes, and pump B can empty [#permalink]  09 Jan 2018, 02:11
1
KUDOS
Choose a random number for a and b suppose A=10 and B=5

A can do 1/10 work in 1 min
B can do 1/5 work in 1 min

There is 1 work to do. Since A comes in and does 1/10 work by working alone for 1 min
The remaining work is 10/10-1/10=9/10
If A and B work together they can do 15/50 work in 1 min so they will take 50/15 minutes to complete the total work
However they only have to do 9/10 of the total work so they can complete the total work in 50/15* 9/10 = 3 mins
total time taken 1 min for A and 3 min for A+B = 4 minutes

Replace the value of A=10 and B=5 in the answer choices option B gives 4
This process can take more than 2 minutes but it is just another way of solving the question
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Re: Pump A can empty a pool in A minutes, and pump B can empty   [#permalink] 09 Jan 2018, 02:11
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