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23 Sep 2023, 11:43
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Three boys and four men can complete a job together in 8 days. If the work rate of each woman is twice that of a boy and two-thirds that of a man, how many days will it take for six women to complete the same job?
A. 5 5/9 days
B. 6 days
C. 10 days
D. 12 days
E. 15 days
A. 5 5/9 days
B. 6 days
C. 10 days
D. 12 days
E. 15 days
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23 Sep 2023, 12:14
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Bunuel
Three boys and four men can complete a job together in 8 days. If the work rate of each woman is twice that of a boy and two-thirds that of a man, how many days will it take for six women to complete the same job?
A. 5 5/9 days
B. 6 days
C. 10 days
D. 12 days
E. 15 days
A. 5 5/9 days
B. 6 days
C. 10 days
D. 12 days
E. 15 days
Units of work done by 1 boy = \(b\)
Units of work done by 1 men = \(m\)
Work done per day by 3 boys and 4 men = \(3b + 4m\) units
Work done by 3 boys and 4 men in 8 days = Total Work = \(8*(3b + 4m) = 24b + 32m\) units
Assume that each woman does \(w\) units of work each day.
"...work rate of each woman is twice that of a boy..."
\(w = 2b\)
\(b = \frac{w}{2}\)
"...two-thirds that of a man..."
\(w = \frac{2}{3}m\)
\(m = \frac{3}{2}w\)
We can use the values to find the total units of work in terms of \('w'\)
\(8*(3b + 4m) = 24b + 32m = 24*(\frac{w}{2}) + 32*(\frac{3}{2}w) = 60w\)
Work done by \(6\) women per day = \(6w\)
Number of days = \(\frac{60w}{6w} = 10\)
Option C
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Schools: Anderson '26 (A$) Foster (A$$) Fuqua '26 (WL) Marshall '26 (WL) McCombs '26 (A$) Ross '26 (A$) Tepper '26 (WL) Goizueta '26 (A$$$) Kelley '26 (M$$$$) Kenan-Flagler '26 (A$$$) Scheller '26 (A$$$$)
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23 Sep 2023, 12:46
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Setting up the equation for men and boys :-
3/B+4/M=1/8
Given data about the rate of each women :-
2/B=2/3M
B=3M
Therefore,
3/3M+4/M=1/8
M=40
Rate of 6 women :-
2/3M = (2/3*120)*6 = 1/10
Time = 10 days.
Posted from my mobile device
3/B+4/M=1/8
Given data about the rate of each women :-
2/B=2/3M
B=3M
Therefore,
3/3M+4/M=1/8
M=40
Rate of 6 women :-
2/3M = (2/3*120)*6 = 1/10
Time = 10 days.
Posted from my mobile device
