1. **Stating the problem:** Make $t$ the subject of the relation $$\frac{8}{t} = w + \frac{m}{n}$$ 2. **Formula and rules:** To make $t$ the subject, we need to isolate $t$ on one side of the equation. This involves algebraic manipulation such as addition, subtraction, multiplication, division, and taking reciprocals. 3. **Step-by-step solution:** - Start with the equation: $$\frac{8}{t} = w + \frac{m}{n}$$ - Combine the right side into a single fraction: $$w + \frac{m}{n} = \frac{wn}{n} + \frac{m}{n} = \frac{wn + m}{n}$$ - So the equation becomes: $$\frac{8}{t} = \frac{wn + m}{n}$$ - Cross-multiply to isolate $t$: $$8n = t(wn + m)$$ - Divide both sides by $(wn + m)$: $$t = \frac{8n}{wn + m}$$ 4. **Final answer:** $$t = \frac{8n}{wn + m}$$