Dane:
v1 = 20km/h
v2 = 30km/h
droga w jedną stronę = S = [tex]\frac{1}{2}[/tex]s
droga w dwie strony = 2S = s
Szukane:
v = ?
t - całkowity czas w dwie strony
v = [tex]\frac{s}{t\\}[/tex] --> s = v * t
[tex]\frac{1}{2}[/tex]s = v1 * t1 czyli:
t1 = [tex]\frac{1}{2}[/tex]s/ v1, więc t2 = [tex]\frac{1}{2}[/tex]s / v2
t = t1 + t2, więc:
[tex]\frac{\frac{1}{2}s }{v1} + \frac{\frac{1}{2}s }{v2} = \frac{\frac{1}{2}s * v2 }{v1*v2} + \frac{\frac{1}{2}s * v1 }{v2*v1} =\frac{\frac{1}{2}s * v1 +\frac{1}{2}s * v2 }{v2*v1}= \frac{\frac{1}{2}s(v1+v2) }{v1*v2}[/tex]
[tex]v = \frac{s}{\frac{\frac{1}{2}s(v1+v2) }{v1*v2}} =\frac{2}{\frac{\\v1+v2 }{v1*v2}}[/tex]
[tex]\frac{2}{\frac{\\v1+v2 }{v1*v2}} = \frac{2*v1*v2}{v1+v2} = \frac{2*20km/h*30km/h}{20km/h+30km/h}=\frac{1200km/h}{50km/h} = 24km/h[/tex]
