1. **Stating the problem:** We want to find the time it takes to separate 0.24 g of copper at a current strength of 1 ampere, given that 0.12 g of copper separates in 15 minutes at 0.4 ampere. 2. **Formula and principle:** The amount of copper separated ($m$) is directly proportional to both the current strength ($I$) and the time ($t$). This can be written as: $$m \propto I \times t$$ or $$m = k \times I \times t$$ where $k$ is the proportionality constant. 3. **Find the constant $k$ using the given data:** Given $m = 0.12$ g, $I = 0.4$ A, and $t = 15$ minutes, $$0.12 = k \times 0.4 \times 15$$ Simplify: $$0.12 = k \times 6$$ Divide both sides by 6: $$k = \frac{0.12}{6} = 0.02$$ 4. **Use $k$ to find the time $t$ for $m = 0.24$ g and $I = 1$ A:** $$0.24 = 0.02 \times 1 \times t$$ Simplify: $$0.24 = 0.02t$$ Divide both sides by 0.02: $$t = \frac{0.24}{0.02}$$ $$t = 12$$ minutes 5. **Answer:** It takes 12 minutes to separate 0.24 g of copper at 1 ampere.