Question

A landscaper estimates that a set of plants can be installed in 6 hours by 12 workers. The landscaper wants to finish a set of plants in 4 hours. Assuming that the variables are inversely related, how many workers should the landscaper bring to the job?

Answer 1

He should actually bring 18 workers for the job.

Answer 2

18 workers should the landscaper bring to the job to finish a set of plants in 4 hours.

Explanation:

As given

Assuming that a set of plants can be installed in number of hours inversely related to the number of workers.

Let us assume that the number of hours needed for set up a plant be x.

Let us assume that the number of worker needed for setup a plant be y.

Thus

`x \propto (1)/(y)`

`x = (k)/(y)`

Where k is the constant of proportionality.

As given

A landscaper estimates that a set of plants can be installed in 6 hours by 12 workers.

x = 6 , y = 12

Thus

`6 = (k)/(12)`

`6* 12 = k`

k = 72

As given

The landscaper wants to finish a set of plants in 4 hours.

x = 4 , k = 72

Thus

`4= (72)/(y)`

`y= (72)/(4)`

y = 18

Therefore 18 workers should the landscaper bring to the job to finish a set of plants in 4 hours.