On a bicycle 5

Klára left Hořické náměstí on her bicycle and rode to Hradec Králové at an average speed of 20 km/h. Jenda left the same square on his bicycle 15 minutes after Klára left and moved in the same direction as Klára at an average speed of 30 km/h. How long did it take Jenda to catch up with Klára?

Final Answer:

t =  45 min

Step-by-step explanation:

$$\begin{gathered} v_1=20\text{km/h} \\ {v}_2=30\text{km/h} \\ \Delta t=15\text{min}\to \text{h}=15:60\text{h}=0.25\text{h} \\ {s}_1=s_2 \\ {v}_1\cdot x=v_2\cdot (x-\Delta t) \\ 20\cdot x=30\cdot (x-0.25) \\ 10x=7.5 \\ x=\frac{7.5}{10}=0.75 \\ x=\frac{3}{4}=0.75 \\ t=x\to \text{min}=x\cdot 60\text{min}=0.75\cdot 60\text{min}=45\text{min}=45\text{min} \end{gathered}$$

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