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# Two mail sorters, P and Q, work at constant rates. If P can sort x le

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Math Expert
Joined: 02 Sep 2009
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Two mail sorters, P and Q, work at constant rates. If P can sort x le  [#permalink]

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22 Feb 2018, 20:01
00:00

Difficulty:

5% (low)

Question Stats:

90% (01:12) correct 10% (01:54) wrong based on 65 sessions

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Two mail sorters, P and Q, work at constant rates. If P can sort x letters in 60 minutes and Q can sort x letters in 30 minutes, how long will it take (expressed in minutes) for both sorters, working together but independently, to sort x letters?

(A) 45

(B) 20

(C) 15

(D) 10

(E) 3

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Two mail sorters, P and Q, work at constant rates. If P can sort x le  [#permalink]

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22 Feb 2018, 20:36
Bunuel wrote:
Two mail sorters, P and Q, work at constant rates. If P can sort x letters in 60 minutes and Q can sort x letters in 30 minutes, how long will it take (expressed in minutes) for both sorters, working together but independently, to sort x letters?

(A) 45

(B) 20

(C) 15

(D) 10

(E) 3

As P can sort x letters in 60 minutes, P will sort $$\frac{1}{60}$$ letters in a minute
As Q can sort x letters in 30 minutes, Q will sort $$\frac{1}{30}$$ letters in a minute

Together, P and Q sort $$\frac{1}{60} + \frac{1}{30} = \frac{3}{60} = \frac{1}{20}$$ letters in a minute

Therefore, the time taken by both the workers to sort x letters is 20 minutes(Option B)
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Re: Two mail sorters, P and Q, work at constant rates. If P can sort x le  [#permalink]

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22 Feb 2018, 23:05
Lets consider X = 60 (I chose 60 for convenience)

P can sort 60 letters in 60 minutes.
Q can sort 60 letters in 30 minutes.

Both working together can sort 60 letters in 20 minutes.

Ans: 20
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Re: Two mail sorters, P and Q, work at constant rates. If P can sort x le  [#permalink]

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22 Feb 2018, 23:39
1
Bunuel wrote:
Two mail sorters, P and Q, work at constant rates. If P can sort x letters in 60 minutes and Q can sort x letters in 30 minutes, how long will it take (expressed in minutes) for both sorters, working together but independently, to sort x letters?

(A) 45

(B) 20

(C) 15

(D) 10

(E) 3

Say P sorts 60 letters in 60 mins so 1 letter every min. Then Q sorts 2 letters every min. So together they sort 3 letters every min.
To sort 60 letters, they will need 20 mins.

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Re: Two mail sorters, P and Q, work at constant rates. If P can sort x le  [#permalink]

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23 Feb 2018, 00:46
Bunuel wrote:
Two mail sorters, P and Q, work at constant rates. If P can sort x letters in 60 minutes and Q can sort x letters in 30 minutes, how long will it take (expressed in minutes) for both sorters, working together but independently, to sort x letters?

(A) 45

(B) 20

(C) 15

(D) 10

(E) 3

efficiency of P =1/60
Q = 1/30

P+q = 1/60 + 1/30 = 1+2/60 = 3/60 = 1/20

(B) imo
Re: Two mail sorters, P and Q, work at constant rates. If P can sort x le &nbs [#permalink] 23 Feb 2018, 00:46
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