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mendelay
If w women can do a job in d days, then how many days will it take (w + n) women to do the job if all the women work at the same pace?

A. \(\frac{dw}{n+w}\)

B. \(\frac{n+w}{d}\)

C. \(\frac{n+w}{dw}\)

D. \(\frac{d}{n+w}\)

E. \(\frac{d(n+w)}{w}\)

rate of 1 woman=1/dw
rate of n+w women=n+w/dw
inverting, time for n+w women=dw/n+w days
A
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mendelay
If w women can do a job in d days, then how many days will it take (w + n) women to do the job if all the women work at the same pace?

A. \(\frac{dw}{n+w}\)

B. \(\frac{n+w}{d}\)

C. \(\frac{n+w}{dw}\)

D. \(\frac{d}{n+w}\)

E. \(\frac{d(n+w)}{w}\)
1. 1 woman can do the job is dw days
2. w+n women can do the job is dw/(w+n) days
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Could someone explain the flaw in this approach please:

RateWomen x Time = Work Done

Rw X d = 1
Rw = 1/d

(w+n)*1/d x T = 1
(w+n)/d x T = 1
T = d/w+n

I am getting Ans. D

:/
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PierTotti17
Could someone explain the flaw in this approach please:

RateWomen x Time = Work Done

Rw X d = 1
Rw = 1/d

(w+n)*1/d x T = 1
(w+n)/d x T = 1
T = d/w+n

I am getting Ans. D

:/

w women take d days to complete 1 work. What is Rw here? Rate of work of 1 woman or w women?
Or is it R*w (R the rate of each woman and w the number of women?)
If that were the case, R = 1/dw (Rate of each woman)

(w + n)*(1/dw) * Time = 1

Time = dw/(w + n)

Answer (A)

Alternatively, one could plug in numbers:

I say, n = 0. So the work will be done by w+n women in d days. Plugging n = 0 in options, only (A) and (E) give us d.

Next, say 1 woman completes the work in 1 day. 2 women (n = 1) will do it in 1/2 day. Plugging in options (A) and (E), only option (A) gives 1/2

Answer (A)
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VeritasKarishma
PierTotti17
Could someone explain the flaw in this approach please:

RateWomen x Time = Work Done

Rw X d = 1
Rw = 1/d

(w+n)*1/d x T = 1
(w+n)/d x T = 1
T = d/w+n

I am getting Ans. D

:/

w women take d days to complete 1 work. What is Rw here? Rate of work of 1 woman or w women?
Or is it R*w (R the rate of each woman and w the number of women?)
If that were the case, R = 1/dw (Rate of each woman)

(w + n)*(1/dw) * Time = 1

Time = dw/(w + n)

Answer (A)

Alternatively, one could plug in numbers:

I say, n = 0. So the work will be done by w+n women in d days. Plugging n = 0 in options, only (A) and (E) give us d.

Next, say 1 woman completes the work in 1 day. 2 women (n = 1) will do it in 1/2 day. Plugging in options (A) and (E), only option (A) gives 1/2

Answer (A)

Hi VeritasKarishma,

w women take d days to complete 1 work. What is Rw here? Rate of work of 1 woman or w women?
Or is it R*w (R the rate of each woman and w the number of women?)
If that were the case, R = 1/dw (Rate of each woman)

In my mind, I am doing: Rate of Women x Time = Work

I guess my mistake is that I need to take into consideration the INDIVIDUAL work done by each woman. It's just confusing in my head because the question stem says: "if w women do a job in d days.." doesn't that imply that the Rate is of the collective women? Not sure why we have to take each individual one.

But thank you for the reply! This is something I would 100% get wrong on the test due to some confusing wording.
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W1 / M1 * D1 = W2 / M2 * D2

Let t be the required time taken by (n+w) people
=> 1 / wd = 1 / (w+n) * t
=> t = wd / (w+n)­

A is the ans.
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