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Current Student B
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Re: If w women can do a job in d days, then how many days will  [#permalink]

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1) First of all we need to set up an equation for w women and find the rate for each woman: $$w*r*d=1; r=\frac{1}{wd}$$
2) Now let's set up an equation for (w+n) women: $$(w+n)*\frac{1}{wd}*T=1; T=\frac{1}{(w+n)/wd}=\frac{wd}{w+n}$$
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Re: If w women can do a job in d days, then how many days will  [#permalink]

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1
mendelay wrote:
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. $$\frac{d(n+w)}{w}$$

We are given that w women can do a job in d days. Thus, the rate of the w women is 1/d.
Next we need to determine the rate of (w + n) women. To calculate that rate, we can use the following proportion in which the value in each numerator is the number of women and the value in each denominator is the corresponding rate, and we can let r = the rate of the (w + n) women:

w/(1/d) = (w+n)/r

dw = (w+n)/r

dwr = (w + n)

r = (w + n)/dw

Finally, we need to determine the time it will take (w+n) women to complete 1 job. Since time = work/rate, we can create the following equation:

time = 1/[(w + n)/dw]

time = dw/(w + n)

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Re: If w women can do a job in d days, then how many days will  [#permalink]

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M1D1=M2D2
w*d=(w+n)*D2
D2=wd/(w+n)

M=no of women
D= no of days

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If w women can do a job in d days, then how many days will  [#permalink]

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mendelay wrote:
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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Re: If w women can do a job in d days, then how many days will  [#permalink]

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mendelay wrote:
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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Re: If w women can do a job in d days, then how many days will  [#permalink]

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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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Re: If w women can do a job in d days, then how many days will  [#permalink]

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PierTotti17 wrote:
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)

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

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Re: If w women can do a job in d days, then how many days will  [#permalink]

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PierTotti17 wrote:
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)

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

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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Re: If w women can do a job in d days, then how many days will  [#permalink]

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_________________ Re: If w women can do a job in d days, then how many days will   [#permalink] 19 Feb 2020, 06:59

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