Lukas Jakub pursuit

Luke left the Tereza cottage and walked at an average 4 km/h speed. Forty-five minutes later, Jacob followed him on a bicycle from the same cottage. He followed Luke's route and caught up with him after 20 minutes. What was Jacob's average speed?

Final Answer:

v₂ =  13 km/h

Step-by-step explanation:

$$\begin{gathered} v_1=4\text{km/h} \\ {t}_1=45\text{min}\to \text{h}=45:60\text{h}=0.75\text{h} \\ {t}_2=20\text{min}\to \text{h}=20:60\text{h}=0.33333\text{h} \\ {s}_1=v_1\cdot (t_1+t_2)=4\cdot (0.75+0.3333)=\frac{13}{3}\doteq 4.3333\text{km} \\ {s}_1=s_2 \\ {s}_1=s_2=v_2\cdot t_2 \\ {v}_2=\frac{s_1}{t_2}=\frac{4.3333}{0.3333}=13\text{km/h} \end{gathered}$$

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