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
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.
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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