One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them four hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?

(A) 5/7
(B) 1
(C) 10/7
(D) 12/7
(E) 22/7

D. 12/7

Step-by-step explanation:

The first thing is to define the variables of each one,

Let W be the rate for a woman

Let M be the rate for a man

Let G be the rate for a girl

According to the statement, we have to:

W + M = 1/2

W + 2 * G = 1/2

M + G = 1/4

Now if we add all the previous equations:

2 * W + 2 * M + 3 * G = 5/4

We have that there is a common factor 2

2 * (W + M + (3/2) * G) = 5/4

In the end we have:

W + M + 1.5 * G = 5/8

From which we can lower the following:

Time required would be the inverse of the equation, that is:

1 / W + 1 / M + (2/3) * G = 8/5

Therefore 8/5 = 1.6

BUT we need 1G and we have more 0.5G. Which implies that the time will be little more than 1.6.

If we check the answers

Options A, B, C are less than 1.6. Delete them.

Option E is more than 2 hours. It is an exaggerated time, since it is only 0.5 more time and should logically be less than 2 hours when all of them combined work together. Delete E

The only answer that remains, would be the correct one, that is, D 12/7, which is a little greater than 1.6.

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step-by-step explanation: