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 7 volunteers 1.25 hours to clean up the park, which of the following equations models this situation?

Answer 1

Answer:

$C. \ t=\frac{8.75}{v}$

Step-by-step explanation:

Given the time t it takes for a group of volunteers to clean up a park varies inversely with the number of volunteers v.

Therefore, we could write in inverse relation between t and v as

$t=\frac{k}{v}$, where k is the constant of proportionality.

We also given if it takes 7 volunteers 1.25 hours to clean up the park.

Therefore, plugging t=1.25 and and v=7 in above inverse relation, we get

$1.25=\frac{k}{7}$

On cross multiplying, we get

$1.25 \times 7 = k$

k= 8.75.

So, we got value of the constant of proportionality = 8.75.

Plugging k= 8.25 in inverse relation, we get

$t=\frac{8.75}{v}$, which is c option.

Answer 2

T ∝ 1/v 

so, t = k/v or tv = k 

Then, with t = 2.5 and v = 5 we have: 

2.5 = k/5 

so, k = 12.5 

Therefore, t = 12.5/v or vt = 12.5  HOPE IT HELPED