[tex]Vs=\frac{s}{t} ~~gdzie~~ t=t_{1}+t_{2}+t_{3} ~~\land~~s= s_{1}+s_{2}+s_{3} \\\\V=\frac{s}{t} ~~\Rightarrow~~t=\frac{s}{V} \\\\I.~~V_{1} =40\frac{km}h} ~~\land~~s_{1}= \frac{1}{3} s~km~~\Rightarrow~~t_{1}=\frac{s}{3V_{1} } ~h\\\\II.~~V_{2} =50\frac{km}h} ~~\land~~s_{2}= \frac{1}{3} s~km~~\Rightarrow~~t_{2}=\frac{s}{3V_{2} } ~h\\\\III.~~V_{3} =90\frac{km}h} ~~\land~~s_{3}= \frac{1}{3} s~km~~\Rightarrow~~t_{3}=\frac{s}{3V_{3} } ~h\\\\Vs=\frac{s_{1}+s_{2}+s_{3} }{t_{1}+t_{2}+t_{3} } \\\\[/tex]
[tex]Vs=\frac{s}{\frac{s}{3V_{1}}+\frac{s}{3V_{2} }+\frac{s}{3V_{3} } }[/tex]
[tex]Vs=\frac{s}{s(\frac{1}{3V_{1} }+\frac{1}{3V_{2} }+\frac{1}{3V_{3} }) } \\\\Vs=\frac{1}{\frac{V_{2} V_{3} +V_{1} V_{3} +V_{1} V_{2} }{3V_{1} V_{2} V_{3} } } \\\\Vs=\frac{3V_{1} V_{2} V_{3}}{V_{2} V_{3} +V_{1} V_{3} +V_{1} V_{2} } \\\\[/tex]
[tex]Vs=\frac{3V_{1} V_{2} V_{3}}{V_{2} V_{3} +V_{1} V_{3} +V_{1} V_{2} }~~\land~~V_{1} =40\frac{km}{h} ~~\land~~V_{2} =50\frac{km}{h}~~\land~~V_{3} =90\frac{km}{h}\\\\Vs=\frac{540 ~000}{(4~500+3~600+2~000)} ~~[\frac{\frac{km^{3} }{h^{3} } }{\frac{km^{2} }{h^{2} } } ]\\\\Vs=\frac{540~000}{10~100} ~~[\frac{km^{3} }{h^{3} } \cdot\frac{h^{2} }{km^{2} } ]\\\\Vs \approx 53,46~\frac{km}{h}[/tex]
