Question

If 10 workers take eight hours to sew a stores order of pants, then how long would 15 workers take to sew the stores order of pants? Assume all workers work at the same steady rate and all the pants are the same. Part A.) Is the proportion 8hours/10 workers = Xhours/15 workers appropriate for solving the sewing problem why or why not? Part B.) explain how to reason about multiplication and division with quantities to solve the sewing problem

Answer 1

According to the given data we have the following proportion:

8hours/10 workers = Xhours/15 workers

A) The above proportion is not appropiate for solving the problem.

Since, the relationship between the number of workers and the time taken for sewing is an inverse relation:

The above proportion is just a direcly proportional relation.

B). As I stated above the relationship between the number of workers and the time taken for sewing is an inverse relation, hence, if the number of workers doubles then the number of time taken reduces to half.

So, since 15=10*15/10

therefore, time taken for 15 workers to sew pants is:

8/ 15/10 = 8* 10/15

=5 1/3 hours.

The time taken for 15 workers to sew pants is 5 1/3 hours.