Question

The amount of time t it takes for a group of volunteers to clean up a park varies inversely with the number of volunteers v. If it takes 5 volunteers 2.5 hours to clean up the park, which of the following equations models this situation

Answer 1

t = k/v 1.5 = k/7 k = 10.5 so we have : t = 10.5/v

Answer 2

`v*t=12.5` or
`v=12.5/t` or
`t=12.5/v`

Explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
`y*x=k` or
`y=k/x`

Let

v-------> the numbers of volunteers

t-------> the amount of time

Find the constant k

`v*t=k`

we have

`t=2.5\ hours,v=5\ volunteers`

substitute

`5*2.5=k`

`k=12.5`

the equation that models the situation is equal to

`v*t=12.5` or
`v=12.5/t` or
`t=12.5/v`