Question

The time it takes to remodel a kitchen t(p) varies inversely with the number of workers assigned to the job p. A kitchen remodeling job takes 40 hours to complete when 2 workers are assigned to it. Which equation can be used to find the time to complete the job when p workers are assigned to it.

A. t(p)=40p
B. t(p)=8p
C. t(p)=80/p
D. t(p)=20/p

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation}\\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf \textit{\underline{t(p)} varies inversely with \underline{p}}\qquad t(p)=\cfrac{k}{p} \\\\\\ \textit{we also know that } \begin{cases} t(p)=40\\ p=2 \end{cases}\implies 40=\cfrac{k}{2}\implies 80=k \\\\\\ therefore\qquad \boxed{t(p)=\cfrac{80}{p}}$