JAMB 1991 · UME · Q15✱✱

If $w$ varies inversely as $\frac{uv}{u + v}$ and $w = 8$ when $u = 2$ and $v = 6$ , find a relationship between $u$ , $v$ and $w$ .

Worked solution (try it first)

Inverse variation: $w = \dfrac{k}{uv/(u + v)}$ , which turns over to $w = \dfrac{k(u + v)}{uv}$ .
Put in $u = 2$ , $v = 6$ , $w = 8$ : $8 = \dfrac{8k}{12}$ , so $k = 12$ .
So $w = \dfrac{12(u + v)}{uv}$ .
Multiply both sides by $uv$ : $uvw = 12(u + v)$ , option C.