Doubling your velocity Suppose you were to run one lap around an olympic oval with a given distance $d$, over time $t$ with velocity $v_1=d/t$. For your second lap, how fast must you travel so that your average velocity _across both laps_ is twice your velocity during the first lap?

To double your speed you would have to complete two laps - a distance of $2d$ - in time $t$. But you have already spent time $t$ in travelling a distance of $d$ (your first lap), So ...