Car meeting calculation

At midnight, a 40km/h truck will leave České Budějovice for Turnov. At 1.5 hours after midnight, a 70 km/h car drove against him. The distance between České Budějovice and Trutnov is 223 km. At what time and how far from Trutnov will the two cars meet?

Result

T = 2:59 hh:mm
s₂ =  103.7273 km

Step-by-step explanation:

$$\begin{gathered} s_1+s_2=223 \\ {s}_1=40\cdot t \\ {s}_2=70\cdot (t-1.5) \\ {s}_1+s_2=223 \\ {s}_1-40t=0 \\ {s}_2-70t=-105 \\ Row2-Row1\to Row2 \\ -s_2-40t=-223 \\ Row3+Row2\to Row3 \\ -110t=-328 \\ t=\frac{-328}{-110}=2.98181818 \\ {s}_2=\frac{-223+40t}{-1}=\frac{-223+40\cdot 2.98181818}{-1}=103.72727273 \\ {s}_1=223-s_2=223-103.72727273=119.27272727 \\ {s}_1=\frac{1312}{11}\doteq 119.272727 \\ {s}_2=\frac{1141}{11}\doteq 103.727273 \\ t=\frac{164}{55}\doteq 2.981818 \\ T=t=2.9818=2.98182=2:59\text{hh}:\text{mm} \end{gathered}$$

$s_2=103.7273=103.7273\text{km}$

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