One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them four hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?
(A) 5/7
(B) 1
(C) 10/7
(D) 12/7
(E) 22/7
Answer: D
Source: Veritas Prep
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One woman and one man can build a wall together in two hours,
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BTGModeratorVI
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One approach is to determine the size of the jobBTGModeratorVI wrote: ↑Fri Aug 14, 2020 1:12 pmOne woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them four hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?
(A) 5/7
(B) 1
(C) 10/7
(D) 12/7
(E) 22/7
Answer: D
Source: Veritas Prep
One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time.
The part in blue tells us that 2 girls have the same output as 1 man.
So, let's say that 1 girl has an output of 1 unit per hour
This means that 1 man has an output of 2 units per hour
So, COMBINED, 1 man and 1 girl have an output of 3 units per hour
If one man and one girl worked together, it would take them four hours to build the wall.
Working together, 1 man and 1 girl have an output of 3 units per hour
So, after 4 hours, their combined output is 12 units.
In other words, we can say that the entire job consists of 12 units.
One woman and one man can build a wall together in two hours
Since 1 man has an output of 2 units per hour, in two hours the man's output will be 4 units.
The entire job consists of 12 units, so the woman completed the other 8 units (in 2 hours).
So, 1 woman has an output of 4 units per hour
How many hours would it take one woman, one man, and one girl, working together, to build the wall?
We have:
1 girl has an output of 1 unit per hour
1 man has an output of 2 units per hour
1 woman has an output of 4 units per hour
And the entire job consists of 12 units.
The combined rate of all 3 workers = 1 + 2 + 4 = 7 units per hour
So, the time to complete the job = 12/7 hours
Answer: D
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One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time.BTGModeratorVI wrote: ↑Fri Aug 14, 2020 1:12 pmOne woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them four hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?
(A) 5/7
(B) 1
(C) 10/7
(D) 12/7
(E) 22/7
Since replacing 1 man with 2 girls does not change the amount of time required to complete the job, 1 man is the equivalent of 2 girls:
M = 2G.
Let G = 1 unit per hour, implying that M = 2 units per hour.
If one man and one girl worked together, it would take them four hours to build the wall.
Since M+G = 2+1 = 3 units per hour, the resulting wall produced in 4 hours = 3*4 = 12 units.
One woman and one man can build a wall together in two hours.
Since the 12-unit wall is built in 2 hours, we get:
W+M = 12/2 = 6 units per hour.
Since M = 2 units per hour, W = 4 units per hour.
How many hours would it take one woman, one man, and one girl, working together, to build the wall?
Since W+M+G = 4+2+1 = 7 units per hour, the time to build the 12-unit wall = 12/7 hours.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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