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)

Answer: A
_________________

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

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

:/

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.