Janka Katka meeting

Jane and Kate live in villages 16 km away. They agreed to meet precisely halfway. Jane was driving at a speed of 4 km/h. Kate came out 30 minutes later. At what speed must Kate drive to fulfill the agreement?

Final Answer:

v₂ =  5.3333 km/h

Step-by-step explanation:

$$\begin{gathered} s=16\text{km} \\ {v}_1=4\text{km/h} \\ {t}_0=30\text{min}\to \text{h}=30:60\text{h}=0.5\text{h} \\ {v}_1\cdot t=s/2 \\ t=\frac{s}{2\cdot v_1}=\frac{16}{2\cdot 4}=2\text{h} \\ {v}_2\cdot (t-t_0)=s/2 \\ {v}_2=\frac{s}{2\cdot (t-t_0)}=\frac{16}{2\cdot (2-0.5)}=5.3333\text{km/h} \end{gathered}$$

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