An alternate approach for a problem in a locked thread:

**Quote:**

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

b. 4

c. 5

d. 6

e. 7

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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