Drum: x km
I zi:
[tex] \frac{1}{6} \times x = \frac{x}{6} km[/tex]
Rest:
[tex]x - \frac{x}{6} = \frac{6x}{6} - \frac{x}{6} = \frac{5x}{6} km[/tex]
II zi:
[tex] \frac{3}{5} \times \frac{5x}{6} = \frac{x}{2} km[/tex]
Rest:
[tex] \frac{5x}{6} - \frac{x}{2} = \frac{5x}{6} - \frac{3x}{6} = \frac{2x}{6} = \frac{x}{3} km[/tex]
III zi:
[tex] \frac{1}{2} \times \frac{x}{3} = \frac{x}{6} km[/tex]
IV zi: 50 km
Total:
[tex] \frac{x}{6} + \frac{x}{2} + \frac{x}{6} + 50 = x \\ \frac{2x}{12} + \frac{6x}{12} + \frac{2x}{12} + \frac{600}{12} = \frac{12x}{12} \\ 2x + 6x + 2x + 600 = 12x \\ 600 = 12x - 2x - 6x - 2x \\ 600 = 2x \\ x = \frac{600}{2} = > x = 300 \: km[/tex]
I zi:
[tex] \frac{300}{6} = 50 \: km[/tex]
II zi:
[tex] \frac{300}{2} = 150 \: km[/tex]
III zi:
[tex] \frac{300}{6} = 50 \: km[/tex]
