Six men and one woman can complete a job in 2 days. Three men and

Question

Six men and one woman can complete a job in 2 days. Three men and eight women can complete the same job in 1 day. If each man works at the same constant rate and each woman works at the same constant rate, how many days would 1 man and 1 woman, working together, take to complete the job?

A. 4
B. 5
C. 6
D. 7
E. 8

6 men and 1 woman can complete some work in 2 days.3 men and 8 women can complete some work in a day. Find the number of days taken by 1 man and 1 woman to complete this work ?

GraemeGmatPanda · Answer

We create variables to represent the rates of work per day for each man and each woman.
 M = 	ext{rate of one man (jobs per day)} 
 W = 	ext{rate of one woman (jobs per day)}

From  "Six men and one woman can complete a job in 2 days" , we translate the combined rate equation.
 6M + W = \frac{1}{2}

From  "Three men and eight women can complete the same job in 1 day" , we translate the combined rate equation.
 3M + 8W = 1

We isolate  W  in the first equation by subtracting  6M  from both sides.
 W = \frac{1}{2} - 6M

We substitute the expression for  W  into the second equation.
 3M + 8(\frac{1}{2} - 6M) = 1

We expand and combine like terms on the left side to simplify the equation.
 3M + 8(\frac{1}{2} - 6M) = 1 
 3M + 4 - 48M = 1

We isolate the term with  M  by subtracting  4  from both sides.
 3M + 4 - 48M - 4 = 1 - 4 
 -45M = -3

We solve for  M  by dividing both sides by  -45 .
 \frac{-45M}{-45} = \frac{-3}{-45} 
 M = \frac{1}{15}

We substitute  M = \frac{1}{15}  back into the expression for  W .
 W = \frac{1}{2} - 6(\frac{1}{15})

We simplify the fraction  \frac{6}{15}  by canceling common factors.
 \frac{6}{15} = \frac{3	imes2}{3	imes5} = \frac{2}{5}

We subtract the fractions  \frac{1}{2} - \frac{2}{5}  by finding a common denominator.
 \frac{1}{2} - \frac{2}{5} = \frac{5}{10} - \frac{4}{10} = \frac{1}{10}

We find the combined rate of one man and one woman working together.
 M + W = \frac{1}{15} + \frac{1}{10}

We simplify the sum of fractions to find the combined rate.
 \frac{1}{15} + \frac{1}{10} = \frac{2}{30} + \frac{3}{30} = \frac{5}{30} = \frac{1}{6}

We calculate the time to complete one job by taking the reciprocal of the combined rate.
 T = \frac{1}{M + W} = \frac{1}{\frac{1}{6}} = 6

Answer C

Hope this helps! 
ʕ•ᴥ•ʔ

Dereno · Answer

Equating the work , we get

(6m+1w)*2 = (3m + 8w)

12m + 2w = 3m + 8w

9m = 6w

m : w :: 3 : 2

3m = 2 w, substuite in ( 3m + 8w) = 10w complete a job in 1 day.

Hence, 1 w completes a job in 10 days.

Substitute in (12m + 2w) , we get 15m complete a job in 1 day.

1 men take 15 days to complete a job.

Efficiency of women : Men , with the total work as 30 units is 3:2

Total time taken by 1 men and 1 women = 30/ (5) =  6 days.

Option C

Navdeep2000 · Answer

Let's use M to denote Men and W to denote Women.

Using our basic R=A/T formula,
We can deduce this info "Six men and one woman can complete a job in 2 days" to (6/M)+(1/W)=1/2
Simplifying it further, we'd get :
 (2M+12W) = (MW)

Accordingly, we can deduce this info "Three men and eight women can complete the same job in 1 day." to (3/M)+(8/W)=(1/1)
Simplifying it further, we'd get :
 (8M+3W)=(MW)

Now, we can put our equations like this : (2M+12W)=(8M+3W) OR (6M=9W) or  (2M=3W)

We can further simplify it to  M=(3W/2)  and furthermore, solve for M by putting it in our original equations.

After doing so, we'd come at  M=15  and  W=10 .

Since, we are asked how much longer it would take 1 man and 1 woman to complete a job together, we can form this :
(1/15)+(1/10) OR (5/30) OR  (1/6)

Remember, Rate is inversely proportional to the Time and vice versa. So, in our case, we need to flip the rate to get the time i.e.  6 days .

Option C

harshitasinghal · Answer

Hi, 
Is there a faster or better approach than the ones mentioned in the comments. I can't understand those solutions that well.

Krunaal · Answer

Hi, can you please share which part was unclear to you in the above solutions? or your attempt? - that helps the experts to identify the exact difficulty you're facing and solve your doubt better!

suscipitlabore · Answer

Rate of 6M+1W= 1/2 (1)
Rate of 3M + 8 W =1 (2)

adding rates (1) & (2) = 9m + 9w = 3/2 
9(M+W)= 3/2
Dividing both sides by 9
Rate for 1M+1W = 1/6

Thus Time taken = 1/ rate = 6

Six men and one woman can complete a job in 2 days. Three men and

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Six men and one woman can complete a job in 2 days. Three men and

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