All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours. How many hours would this job take if the number of workers:
if the workers
increased by the factor two
whats the answer
To solve this problem, we can use the concept of "worker-hours." The number of worker-hours represents the total amount of work done by the workers.
In the given scenario, we know that six workers can complete the job in 22 hours. So, the total worker-hours required to complete the foundation is 6 workers × 22 hours = 132 worker-hours.
Now, if the number of workers increases by a factor of two, we have to calculate the total worker-hours again.
As the number of workers doubles, the total worker-hours required to complete the same amount of work will be halved. This is because more workers can divide the workload among themselves, reducing the total time required.
So, if we multiply the original number of worker-hours (132) by 1/2 (or divide it by 2), we can find the new number of worker-hours required.
New number of worker-hours = 132 worker-hours ÷ 2 = 66 worker-hours
Therefore, if the number of workers is increased by a factor of two, it would take 66 worker-hours to complete the job.
To determine the number of hours it would take, we need to find out how many workers are required to reach 66 worker-hours. If we assume that all workers still work at the same pace, we can divide the total worker-hours needed by the number of workers.
Let's say the number of workers required is N. We can calculate the number of hours using the equation:
N workers × X hours = 66 worker-hours
We don't know the value of X, the number of hours, so we rearrange the equation:
X hours = 66 worker-hours / N workers
Now, if we plug in a value for N, we can find the corresponding number of hours required to complete the job.
All the members of a construction crew work at the same pace. Six of them working together are able to pour foundation in 22 hours.
How many hours would this job take if the number of workers increased by factor of 4?