1. **State the problem:** Carlos takes 16 minutes to cycle home from work on Wednesday. On Thursday, he cycles the same distance at half the speed. We need to find how long his journey takes on Thursday. 2. **Formula and rules:** Time, speed, and distance are related by the formula $$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$. 3. **Given:** - Time on Wednesday, $t_1 = 16$ minutes - Speed on Thursday, $v_2 = \frac{1}{2} v_1$ (half the speed of Wednesday) - Distance is the same both days, so $d = v_1 \times t_1 = v_2 \times t_2$ 4. **Find:** Time on Thursday, $t_2$ 5. **Calculate:** Using the formula for distance equality, $$d = v_1 \times t_1 = v_2 \times t_2$$ Substitute $v_2 = \frac{1}{2} v_1$: $$v_1 \times t_1 = \frac{1}{2} v_1 \times t_2$$ 6. **Simplify:** Cancel $v_1$ from both sides: $$\cancel{v_1} \times t_1 = \frac{1}{2} \cancel{v_1} \times t_2$$ which gives $$t_1 = \frac{1}{2} t_2$$ 7. **Solve for $t_2$:** $$t_2 = 2 t_1 = 2 \times 16 = 32$$ minutes **Final answer:** Carlos's journey takes 32 minutes on Thursday.