In the parking lot

At a parking lot 20 km from Bratislava thieves stole car A; it is moving at speed V: 130 km/h towards Žilina. After twelve minutes the motorway police received at the beginning of the motorway in Bratislava an order to catch up with the stolen car and stop it. The duty officer of the motorway police has 10 minutes to prepare the action. Before the decision he must process information:
1. A police car with siren moves on the motorway at a speed of 180 km/h, a police helicopter 280 km/h
2. The stolen car must be stopped before Trenčín
3. For cooperation in the arrest, the police unit in the city lying nearest to the place of meeting must be requested (Trnava? Trenčín? Žilina?)

Final Answer:

s₁ =  243.6 km
s₂ =  126.3111 km

Step-by-step explanation:

$$\begin{gathered} v_1=130\text{km/h} \\ p=20\text{km} \\ {v}_2=180\text{km/h} \\ {v}_3=280\text{km/h} \\ d=12+10=22\text{min} \\ T=d\to \text{h}=d:60\text{h}=22:60\text{h}=0.36667\text{h} \\ {s}_1=S_1 \\ t\cdot v_2=p+v_1\cdot (t+T) \\ t\cdot 180=20+130\cdot (t+0.36666666666667) \\ 50t=67.666667 \\ t=\frac{67.66666667}{50}=1.35333333 \\ t=\frac{203}{150}\doteq 1.353333 \\ {s}_1=t\cdot v_2=1.3533\cdot 180=243.6\text{km} \end{gathered}$$

$$\begin{gathered} p+v_1\cdot (x+T)=x\cdot v_3 \\ 20+130\cdot (x+0.36666666666667)=x\cdot 280 \\ 150x=67.666667 \\ x=\frac{67.66666667}{150}=0.45111111 \\ x=\frac{203}{450}\doteq 0.451111 \\ {s}_2=x\cdot v_3=0.4511\cdot 280=126.3111\text{km} \end{gathered}$$

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