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  ewka13 5.1.2011 (16:43)

  v_{1} = 40km/h
  
  v_{2} = 60km/h
  
  s = v_{1}*t_{1} = v_{2}*t_{2}
  
  \frac {v_{1}} {v_{2}} = \frac {t_{2}} {t_{1}}
  
  \frac {t_{2}} {t_{1}} = \frac {40km/h} {60km/h} = \frac {2} {3}
  
  t_{2} = \frac {2} {3} t_{1}
  
  czas ruchu :
  t = t_{1} + t_{2} = t_{1} + \frac {2} {3}t_{1} = \frac {5} {3}t_{1}
  
  prędkość średnia :
  
  v_{sr} = \frac {2s} {t} = \frac {v_{1}t_{1}+v_{2}t_{2}} {t} =
  
  =\frac {v_{1}t_{1}+v_{2}*\frac {2} {3}t_{1}} {\frac {5} {3}t_{1}} =
  
  =\frac{ t_{1}(v_{1} + \frac {2} {3}v_{2})} {\frac {5} {3}t_{1}}=
  
  =\frac {v_{1}+ \frac {2} {3}v_{2}} {\frac {5} {3}} =
  
  =\frac {40km/h + \frac {2} {3}*60km/h} {\frac {5} {3}} =
  
  = (40km/h+40km/h)* \frac {3} {5}= 80km/h*\frac {3} {5}= 48km/h
  
  odp.Średnia prędkość wynosi 48km/h.

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