Answer:
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.
Answer:
12/7 hours
Step-by-step 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
