Runner 6

A runner runs the first lap of a circuit at an average speed of 5 km/h. At what speed must the second lap of the same circuit be run so that the average speed of both laps is 10 km/h?

Final Answer:

v₂ = km/h ∞

Step-by-step explanation:

$$\begin{gathered} v_1=5\text{km/h} \\ v=10\text{km/h} \\ {v}_1=s/t_1 \\ {v}_2=s/t_2 \\ v=\frac{2\cdot s}{t_1+t_2} \\ v\cdot (t_1+t_2)=2\cdot s \\ v\cdot (s/v_1+s/v_2)=2\cdot s \\ v\cdot (1/v_1+1/v_2)=2 \\ v\cdot (v_2+v_1)=2\cdot v_1\cdot v_2 \\ v\cdot v_2+v\cdot v_1=2\cdot v_1\cdot v_2 \\ {v}_2(v-2\cdot v_1)=-v\cdot v_1 \\ {v}_2=\frac{v\cdot v_1}{2\cdot v_1-v} \\ {v}_2=\frac{10\cdot 5}{2\cdot 5-10} \\ {v}_2=\frac{50}{0} \\ {v}_2=\infty \end{gathered}$$

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