If it takes 5 men 20 hours to brick a house, How long will it take 8 men to do the job if they work at the same rate
Each of the 5 men worked 20 hours. What is the total man hours required?
Using that total figure how many hours for 8 men. Obviously it will be less, correct?
8/5 as many men, so 5/8 as much time.
To find out how long it will take 8 men to brick the house, we need to determine the rate at which 5 men can brick the house in hours. Once we have that, we can then calculate the number of hours it will take 8 men to do the job.
Given that 5 men can brick a house in 20 hours, we can determine how much work is done in one hour by dividing the total work by the number of hours. In this case, the total work is equal to the entire house.
The equation to determine the work done in one hour is:
Work in one hour = Total work / Total hours
In this case, the work in one hour is equal to the work done by 5 men, which is equivalent to the work done by 8 men. Therefore, the equation becomes:
Work in one hour = Total work / Total hours
Work in one hour = (House) / 20
Work in one hour = (House) / (5 men)
Now, we can calculate the number of hours it will take 8 men to complete the job:
Work in one hour with 8 men = (House) / (8 men)
Since we already know the work in one hour is the same with both 5 men and 8 men, we can set up an equation to find the time it takes:
(House) / (5 men) = (House) / (8 men)
Now, we can cross-multiply to solve for the time it takes 8 men:
(House) * (8 men) = (House) * (5 men)
8 men * (House) = 5 men * (House)
The number of houses cancels out, leaving us with:
8 men = 5 men
This shows that both sides of the equation are equal, so it does not matter how long it takes for 5 men or 8 men to complete the job. They will both take the same amount of time. Therefore, it will still take 20 hours for 8 men to complete the job.