Question

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

Answer 1

12/7 hours

Explanation:

According to the question, a man and a woman can do a job in 2 hours.

The same job can be completed in 2 hours if one woman and two girls combined their efforts.

And if a man and a girl combined their efforts, it would take them 4 hours to complete the same job.

Let's now work out a solution for this tricky problem

Let's put this in an equation to see what we get

--------1m + 1w = 2 hours

--------1w + 2g = 2 hours

This means that the work rate/output of 2 girls equals to that of just one man

So, let's assume that 1 girl has an output of 1 unit per hour

This means that 1 man has an output of 2 units per hour

So if combined,both 1 man and 1 girl have an output of 3 units per

hour

If one man and one girl worked together, it would take them four

hours to build the wall.

Working together, 1 man and 1 girl have an output of 3 units per

hour

So, after 4 hours, their combined output is 12 units.

In other words, we can say that the entire job consists of 12 units.

One woman and one man can build a wall together in two hours

Since 1 man has an output of 2 units per hour, in two hours the

man's output will be 4 units.

The entire job consists of 12 units, so the woman completed the

other 8 units (in 2 hours).

So, 1 woman has an output of 4 units per hour

The number of hours it would take one woman, one man, and one girl,

working together, to build the wall will be:

1 girl has an output of 1 unit per hour

1 man has an output of 2 units per hour

1 woman has an output of 4 units per hour

And the entire job consists of 12 units.

The combined rate of all 3 workers = 1 + 2 + 4 = 7 units per hour

So, the time to complete the job = 12/7 hours

Answer 2

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.