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
We can PLUG IN THE ANSWERS, which represent how many times a man's output exceeds that of a woman.
When the correct answer is plugged in, 3 men will take 5 fewer days to complete the job than 9 women.
B: 4
Let the rate for each woman = 1 unit per day and the rate for each man = 4 units per day.
Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*4)(6) = 66 units.
Time for 9 women to complete the job = \(\frac{work}{rate-for-9-women} = \frac{66}{(9*1)} = \frac{22}{3} ≈ 7\) days.
Time for 3 men to complete the job = \(\frac{work}{rate-for-3-men} = \frac{66}{(3*4)} = \frac{66}{12} = \frac{11}{2} ≈ 5\) days.
Doesn't work:
Here, 3 men take only about 2 fewer days than 9 women.
Eliminate B.
For 3 men to take 5 fewer days, the rate for each man must INCREASE.
Eliminate A.
D: 6
Let the rate for each woman = 1 unit per day and the rate for each man = 6 units per day.
Since it takes 6 days for 3 women and 2 men to complete the job, the job = (rate for 3 women and 2 men)(6 days) = (3*1 + 2*6)(6) = 90 units.
Time for 9 women to complete the job = \(\frac{work}{rate-for-9-women} = \frac{90}{(9*1)} = \frac{90}{9} = 10\) days.
Time for 3 men to complete the job = \(\frac{work}{rate-for-3-men} = \frac{90}{(3*6)} = \frac{90}{18} = 5\) days.
Success!
Here, 3 men take 5 fewer days than 9 women.
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