virtualanimosity wrote:
It takes 6 days for 3 women and 2 men working together to complete a work.3 men would do the same work 5 days sooner than 9 women.How many times does the output of a man exceed that of a woman?
A. 3 times
B. 4 times
C. 5 times
D. 6 times
E. 7 times
The fastest and easiest way to solve this question was already proposed by IanStewart.
I am trying another algebraic approach.
Denote by
W the rate of a woman, by
M that of a men, and by
T the time it takes 9 women to complete the work.
We have the following equations:
6(3W + 2M) = 9WT = 3M(T-5), or, after reducing by 3,
2(3W + 2M) = 3WT = M(T - 5).We are looking for the ratio
M/W which we can denote by
n. Substituting in the above equations
M = nW, we can write:
2(3W + 2nW) = 3WT = nW(T - 5).Divide through by
W, so
6 + 4n = 3T = nT - 5n. Solving for
T (equality between the last two expressions) we obtain
T=\frac{5n}{n-3}.Taking the equality of the first two expressions, we get
6+4n=\frac{3\cdot{5}n}{n-3}.From the possible answer choices we can deduce that
n must be a positive integer.
We need
\frac{15n}{n-3} to be a positive integer. We can see that
n cannot be odd and it must be greater than 3.
We have to choose between B and D.
Only
n = 6 works.
Answer D.
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