9 men do a piece of work in 28 days. How many men will do it in 56 days?
To find out how many men will do the work in 56 days, we can use the concept of man-days, which is the product of the number of men and the number of days it takes them to complete the work.
Given that 9 men complete the work in 28 days, we can calculate the total man-days required to complete the work:
Total man-days = Number of men * Number of days
Total man-days = 9 men * 28 days
Total man-days = 252 man-days
Now, to find the number of men required to complete the work in 56 days, we can divide the total man-days by the number of days:
Number of men = Total man-days / Number of days
Number of men = 252 man-days / 56 days
Number of men = 4.5 men
Since you cannot have a fraction of a man, we round up to the nearest whole number, so the answer is 5 men.
Therefore, 5 men will be required to complete the work in 56 days.
To find the number of men required to complete a piece of work in a given number of days, you can use the formula:
(Number of men) × (Number of days) × (Work rate of a man) = Constant work rate
In this case, we know that the work rate of 9 men over 28 days is equal to the constant work rate. Therefore:
(9 men) × (28 days) × (Work rate of a man) = Constant work rate
To find the work rate of a man, we divide both sides of the equation by (9 men) × (28 days):
Work rate of a man = Constant work rate / (9 men) × (28 days)
Now we can use this work rate to find the number of men who can complete the work in 56 days. We'll use the same constant work rate (since the piece of work hasn't changed) and the new number of days:
(Number of men) × (56 days) × (Work rate of a man) = Constant work rate
Plugging in the work rate we found earlier:
(Number of men) × (56 days) × (Constant work rate / (9 men) × (28 days)) = Constant work rate
Simplifying:
(Number of men) × (56 days) / (9 men) = 1
(Number of men) = (9 men) × (1) / (56 days)
(Number of men) = 9/56
Therefore, the number of men required to complete the work in 56 days is approximately 0.16, which means it would be impossible to have a fraction of a person working. Therefore, rounding up or down, the answer is either 0 men or 1 man.
Come on, think about it.
If 2 of us can paint a house in 4 days, how long would it take to paint it
by yourself?
What operation did you perform?
Did you notice that 28 is half of 56?
(still trying to visualize that fraction of a man working)
Well... 28 is Half of 56. 56 is a longer period than 28 days. 9 men can complete it in 28. If it will take longer for the completion, there should be more people completing the work.
Therefore, since 28 is half of 56;
9 men will do it in 28 days and
18 men in 56 days