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4 men and 6 women finish a job in 8 days, while 3 men and 7 women fin

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Re: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women fin [#permalink]
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Bunuel wrote:
4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it?

(A) 24
(B) 32
(C) 36
(D) 40
(E) 42

Solution:

If we let x be the rate of one man and y be the rate of one woman. We can create the equations:

4x + 6y = 1/8

and

3x + 7y = 1/10

Multiplying the first equation by 3 and the second equation by 4, we have:

12x + 18y = 3/8 = 15/40

and

12x + 28y = 4/10 = 16/40

Subtracting the top equation from the bottom equation, we have:

10y = 1/40

We see that the rate of 10 women is 1/40 of the job; therefore, it will take them 1/(1/40) = 40 days to complete the job.

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Re: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women fin [#permalink]
ScottTargetTestPrep wrote:
Bunuel wrote:
4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it?

(A) 24
(B) 32
(C) 36
(D) 40
(E) 42

Solution:

If we let x be the rate of one man and y be the rate of one woman. We can create the equations:

4x + 6y = 1/8

and

3x + 7y = 1/10

Multiplying the first equation by 3 and the second equation by 4, we have:

12x + 18y = 3/8 = 15/40

and

12x + 28y = 4/10 = 16/40

Subtracting the top equation from the bottom equation, we have:

10y = 1/40

We see that the rate of 10 women is 1/40 of the job; therefore, it will take them 1/(1/40) = 40 days to complete the job.

Won't 4x + 6y = 1/8 this be Amount of work+Amount of Work= Rate
Shouldn't the LHS and RHS have similar type, eg, Rate in LHS and RHS both ?
Im really confused, any help would be appreciated!
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Re: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women fin [#permalink]
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Re: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women fin [#permalink]
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