BTGModeratorVI wrote: ↑Fri Aug 14, 2020 1:12 pm
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
One approach is to determine the
size of the job
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
