If s varies directly as r and inversely as t and s=10 when r=5 and t=3, for what value of t will s=3 when r=4?

Jul 14, 2017

$t = 8$

Explanation:

$\text{the initial statement is } s \propto \frac{r}{t}$

$\text{to convert to an equation multiply by k the constant of}$
$\text{variation}$

$\Rightarrow s = k \times \frac{r}{t} = \frac{k r}{t}$

$\text{to find k use the condition given}$

$s = 10 \text{ when "r=5" and } t = 3$

$s = \frac{k r}{t} \Rightarrow k = \frac{s t}{r} = \frac{10 \times 3}{5} = 6$

$\text{the equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{s = \frac{6 r}{t}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$s = 3 \text{ when } r = 4$

$s = \frac{6 r}{t}$

$\Rightarrow t = \frac{6 r}{s} = \frac{6 \times 4}{3} = 8$