Question

A building company used 24 workers to prepare a building site. The site measured 30 acres and the work was completed in 10 days.

a) The company is asked to prepare another site measuring 45 acres. The company must complete the work on the new site in 12 days. How many extra workers must they use if they are to meet the deadline?
b) What assumption have you made in your calculations? How does this affect your answers?

Answer 1

30 workers are required.

Step-by-step explanation:

If the site measured 30 acres and was completed in 10 days, then it can be said that on average
`(30)/(10) = 3(acres)/(day)` were made.

Then, 24 workers completed 3 acres / day.

Then,
`(24.workers)/((3acres)/(day)) = (8..Workers * days)/(acre)`

8 workers can complete 1 acre per day

Now to know how many workers are needed to complete 45 acres in 12 days, we multiply:

`8(Workers * days)/(acre)*(45)/(12) (acres)/(days) = 30.workers`.

Finally, 30 workers are required.

To solve this problem it was assumed that everyone worked at the same pace, which may not be true, the fact that some work at a slower or faster pace than another could alter the result, causing them to finish less or more acres by day.