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Question 1024048: If it takes 10 men 12 hours to build a wall how long dose it take 8 men working at the same pace
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the basic formula used in this type of a problem is rate per person * number of people * time = quantity of work produced.
the quantity of work produced here would be 1 wall.
the rate per person needs to be figured out.
the number of people is 10.
the number of hours is 12.
the formula becomes:
r * 10 * 12 = 1
r represent the rate per person.
solve for r to get r = 1 / (10*12) = 1/120.
the rate per person is 1/120 of the job in one hour.
if you have only 8 people working, then the formula becomes:
1/120 * 8 * t = 1
t represents the time.
solve for t to get t = 1/(1/120*8).
this becomes t = 15.
it would take 8 people 15 hours when it takes 10 people 12 hours assuming the workers are working at the same average rate each.
if you were able to see it, you could probably have modeled this as an inverse ratio type problem.
it's an inverse ratio problem because, when the number of workers increases, the number of hours required to complete the job decreases.
assuming that's true, then the formula for inverse ratio is y = k/x.
let y = the number of hours required to complete the job and let x equal to the number of people working.
the formula becomes 12 = k / 10.
solve for k to get k = 120.
when the number of workers is 8, the equation becomes y = 120 / 8 which results in y = 15.
you get the same answer, assuming you were able to determine that this was an inverse ratio type problem and you could have modeled it correctly.
i usually play it on the safe side and go with the basic formula shown above.
if you can remember that this type of problem can be solved as an inverse ratio type problem, and you are confident how to apply it, then the inverse ratio formula seems to be a bit quicker to resolve.
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