MHB Work Rate Problem: 4 Men, 9 Women in 13.388 Days

[NotaMathPerson]

If 18 men or 20 women can do a work in 9 days, in what time can 4 men and 9 men do the same work?

My attempt

D = days required

4/162 + 9/180 = 1/D

D = 13.388 days

Is my solution correct?

Thanks!

 

[Prove It]

If 18 men or 20 women can do a work in 9 days, in what time can 4 men and 9 men do the same work?

My attempt

D = days required

4/162 + 9/180 = 1/D

D = 13.388 days

Is my solution correct?

Thanks!

4 men and 9 men?

 

[MarkFL]

If 18 men or 20 women can do a work in 9 days, in what time can 4 men and 9 men do the same work?

My attempt

D = days required

4/162 + 9/180 = 1/D

D = 13.388 days

Is my solution correct?

Thanks!

From your working, I assume the question is actually:

"In what time can 4 men and 9 women do the same work?"

Your method is good, and the solution correct. A single man will take 162 days to complete the work, while a single woman will take 180 days. So, the amount of the job done by each man in a day is 1/162 and for a woman 1/180, and so with 4 men and 9 woman working, the amount done is:

$$\frac{4}{162}+\frac{9}{180}=\frac{121}{1620}$$

and since this is one day's work, this is equal to 1/D of the work. Hence:

$$D=\frac{1620}{121}\approx13.388$$

 

[NotaMathPerson]

From your working, I assume the question is actually:

"In what time can 4 men and 9 women do the same work?"

Your method is good, and the solution correct. A single man will take 162 days to complete the work, while a single woman will take 180 days. So, the amount of the job done by each man in a day is 1/162 and for a woman 1/180, and so with 4 men and 9 woman working, the amount done is:

$$\frac{4}{162}+\frac{9}{180}=\frac{121}{1620}$$

and since this is one day's work, this is equal to 1/D of the work. Hence:

$$D=\frac{1620}{121}\approx13.388$$

Hello!

The answer in my book says it is $6\frac{1}{20}$ days. Why is that?

 

[MarkFL]

Hello!

The answer in my book says it is $6\frac{1}{20}$ days. Why is that?

If it takes 18 men 9 days to do the work, does it make any sense that it would take 13 people, 9 of which are women (who take slightly longer to do the work) a smaller amount of time?

Did you give the problem exactly as stated?

 

[NotaMathPerson]

If it takes 18 men 9 days to do the work, does it make any sense that it would take 13 people, 9 of which are women (who take slightly longer to do the work) a smaller amount of time?

Did you give the problem exactly as stated?

View attachment 5659

Here is the question from the book. This is from a section of ratio and proportion.

 

[MarkFL]

That answer would make sense if it took 11 men 4 days to do the job and 11 women need 11 days to do the job. But as given, the answer supplied with the problem is just wrong. :)