Question

The time t required to drive a certain distance varies inversely with the speed r. if it takes 4 hours to drive the distance at 35 miles per hour, how long it will take to drive the same distance at 45 miles per hour?
A. about 3.11 hours
B. 140 hours
C. about 5.14 hours
D. 393.75 hours

Answer 1

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

$\bf \stackrel{\textit{time \underline{t} required to drive a certain distance varies inversely with the speed \underline{r}}}{t=\cfrac{k}{r}} \\\\\\ \textit{we also know that } \begin{cases} t=4\\ r=35 \end{cases}\implies 4=\cfrac{k}{35}\implies 4(35)=k \\\\\\ 140=k\qquad therefore\qquad \boxed{t=\cfrac{140}{r}} \\\\\\ \textit{now, when \underline{r} = 45, what is \underline{t}?}\qquad t=\cfrac{140}{45}$