Question

8 men and 6 women do some work in 30 days; 14 men and 10 women do the same work in 20.
How many days will it take 5 men and 5 women?
(assume that men and women take unequal amounts of time)

Answer 1

Ugh, Dad gives hard questions.

Answer 2

Though I know that this is related to inverse relations and all.
I know how to do questions for one guy, but not for so many.

Answer 3

I can guide you on how to do this when you are online.

Answer 4

Think in terms of
rate * time = job

rate is measured in \[\frac{\text{jobs}}{\text{man-days}} \]
set up 2 equations and 2 unknown rates (for men and women). For example, the first equation is
\[ (8 \text{ men} \cdot m \frac{\text{jobs}}{\text{man-days}} + 6 \text{ women} \cdot w \frac{\text{jobs}}{\text{woman-days}})\cdot 30 \text{ days}= 1 \text{ job} \]
Once you find the rates m and w, solve for D in
\[ (5m+5w)*D \text{ days} = 1 \text{ job} \]
The peculiar thing about this problem is that one of the rates is negative! (slows down the work)

Answer 5

@asnaseer Hello!

Answer 6

hi - looks like phi has put down some explanations already - do you understand them?

Answer 7

I tend to do these in a /slightly/ different manner

Answer 8

Okay, please, if you can. :)

Answer 9

ok, you are told that "8 men and 6 women do some work in 30 days"

this means that the work can be done in 1 day if we have "30(8 men and 6 women)"

agreed?

Answer 10

30 times the work force means it is completed in 1/30'th of the time

Answer 11

Yes, agreed.
Sorry... there are some problems in the internet at my end. Please don't mind that. Thank you :)

Answer 12

ok, similarly you are told that "14 men and 10 women do the same work in 20"

this means that the work can be done in 1 day if we have "20(14 men and 10 women)"

agreed?

Answer 13

Yes, agreed again!

Answer 14

ok, next I will represent the "work efficiency" of a man by "m" and that of a women by "w".

this gives us:

30(8m + 6w) = 20(14m + 10w)

Answer 15

OK, I am following. Yes.

Answer 16

we can divide both sides by 10 to get:

3(8m + 6w) = 2(14m + 10w)

Answer 17

which leads to:

w = -2m

Answer 18

Yes... and substitution now, right?

Answer 19

\[3(8m + 6(-2m)) = 2(14m + 10(-2m)) \]Yes?

Answer 20

yes, now substitute this into one of the equations, say this one:

30(8m + 6w) = 30(8m - 12m) = 30 * (-4m) = -120m

Answer 21

that represents the total work units

Answer 22

so 5 men and 5 women would have total work units of:

5(m + w) = 5(m - 2m) = -5m

Answer 23

therefore total days taken will be:

days = (-120m)/(-5m)

Answer 24

hope that makes sense?

Answer 25

if not, try using the method that phi described. use the one that makes most sense to you.

Answer 26

Yes!

Answer 27

gr8! :)

Answer 28

Thank you so much, @asnaseer!

Answer 29

yw :)