Question

If r varies jointly as s and t and inversely as u, and r =18 when s=2, t=3, and u =4, find s when r=6, t=2, and u=4

Answer 1

To find the value of s, we must first set up the equation so that we can get the coefficient of variation. Based on the given, the equation is:

$r=k\frac{st}{u}$

Let's substitute the given values of r, s, t, and u to solve for k.

$\begin{gathered} r=k\frac{st}{u} \\ \\ 18=k(\frac{2\times3}{4}) \\ \\ 18=k(\frac{3}{2}) \\ \\ k=18(\frac{2}{3}) \\ \\ k=12 \end{gathered}$

Now that we know k = 12, we can solve for s.

$\begin{gathered} r=k\frac{st}{u} \\ \\ 6=12(\frac{s\times2}{4}) \\ \\ 6=6s \\ \\ s=1 \end{gathered}$

The answer is: s = 1.