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17 Jul 2018, 04:15
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virtualanimosity
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.
19 Jul 2018, 12:42
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virtualanimosity
We can let the number of days for 1 man to finish the work = m and that for 1 woman = w. Thus, the rate of 1 man = 1/m and the rate of 1 woman = 1/w.
Since it takes 6 days for 3 women and 2 men working together to complete the work, we have:
6(3/w + 2/m) = 1
Since 3 men would do the same work 5 days sooner than 9 women, we have:
1/(3/m) + 5 = 1/(9/w)
m/3 + 5 = w/9
Multiplying the above by 9, we have:
3m + 45 = w
Substituting this into 6(3/w + 2/m) = 1, we have:
6(3/(3m + 45) + 2/m) = 1
6(1/(m + 15) + 2/m) = 1
Multiplying the above by m(m + 15), we have:
6m + 12(m + 15) = m(m + 15)
6m + 12m + 180 = m^2 + 15m
m^2 - 3m - 180 = 0
(m - 15)(m + 12) = 0
m = 15 or m = -12
Since m can’t be negative, m = 15. So w = 3(15) + 45 = 90. We see that it takes a man 15 days to complete the work but 90 days for a woman to complete the same work. So a man’s output is 6 times the output of a woman.
Answer: D
07 Nov 2018, 23:55
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virtualanimosity
Please find attached the solution
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12 Jul 2019, 19:05
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virtualanimosity
We can let m = the number of days a man can complete the work by himself and w = the number of days a woman can complete the work by herself. Thus, 1/m = the rate of a man, and 1/w = the rate of a woman.
We can create the equations
6(3 x 1/w + 2 x 1/m) = 1
and
1/(3 x 1/m) = 1/(9 x 1/w) - 5
Simplifying the first equation, we have:
3/w + 2/m = 1/6
Multiplying the equation by 6wm, we have:
18m + 12w = mw
Simplifying the second equation, we have:
m/3 = w/9 - 5
Multiplying the equation by 9, we have:
3m = w - 45
3m + 45 = w
Substituting this in 18m + 12w = mw, we have:
18m + 12(3m + 45) = m(3m + 45)
18m + 36m + 540 = 3m^2 + 45m
3m^2 - 9m - 540 = 0
m^2 - 3m - 180 = 0
(m - 15)(m + 12) = 0
m = 15 or m = -12
Since m can’t be negative, m = 15. Hence, w = 3(15) + 45 = 90. We see that a man’s rate is 6 times that of a woman’s rate since the number of days a man can complete the job is only 1/6 of the number of days a woman can complete the job.
Answer: D
