Infinite speed

A runner completes her first lap of the track at an average speed of 5 km/h. How fast must she run her second lap so that her overall average speed for both laps is 10 km/h?

Final Answer:

v₂ = km/h ∞

Step-by-step explanation:

$$\begin{gathered} v_1=5\text{km/h} \\ v=10\text{km/h} \\ {v}_1=s/t_1 \\ {v}_2=s/t_2 \\ v=\frac{2\cdot s}{t_1+t_2} \\ v\cdot t_1+v\cdot t_2=2\cdot s \\ v\cdot \frac{s}{v_1}+v\cdot \frac{s}{v_2}=2\cdot s \\ \frac{v}{v_1}+\frac{v}{v_2}=2 \\ {v}_2=v\cdot \frac{1}{2-\frac{v}{v_1}} \\ {v}_2=10\cdot \frac{1}{2-\frac{10}{5}} \\ {v}_2=10\cdot \frac{1}{2-2} \\ {v}_2=10\cdot \frac{1}{0} \\ {v}_2=\infty \end{gathered}$$

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