Mathematics: 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.

Bella manages a volunteer group. The time (T)

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icantspeakengles

24.01.2022

Mathematics

42 Volunteers

Step-by-step 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:

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

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