Question

Bella manages a volunteer group. The time (T) that it takes a group of volunteers to construct a house varies inversely as the number of volunteers (V). It takes 20 volunteers to build a house in 63 hours. Write an equation to model this situation. Next, find how many volunteers it would take to build a house in 30 hours.

Answer 1

42 Volunteers

Explanation:

The time (T) that it takes a group of volunteers to construct a house varies inversely as the number of volunteers (V).

This is written as:

`V \propto (1)/(T) \\$Introducing the variation constant k\\V = (k)/(T)\\$It takes 20 volunteers to build a house in 63 hours.$\\When V=20, T=63\\V = (k)/(T)\\20 = (k)/(63)\\k=20*63=1260\\$Therefore, the equation connecting V and T is:$\\V = (1260)/(T)\\$When T=30 hours, we want to determine the number of volunteers needed V$\\V = (1260)/(30)=42\\$42 Volunteers will be needed.$`