Răspuns
x = [tex]142\frac{34}{53}[/tex] km
Explicație pas cu pas:
Notam x - traseul total
Obtinem ecuatia:
[tex]\frac{x}{9} + [\frac{3}{10}*(x - \frac{x}{9})] + 84 = x[/tex]
[tex]\frac{x}{9} + (\frac{3}{10}*\frac{8x}{9}) + 84 = x[/tex]
[tex]\frac{x}{9} + \frac{27x}{90} + 84 = x[/tex]
[tex]\frac{10x}{90} + \frac{27x}{90} + 84 = x[/tex]
[tex]\frac{37x}{90} + 84 = x[/tex]
[tex]\frac{37x}{90} - \frac{x}{1} = -84[/tex]
[tex]-\frac{53}{90}x = -84[/tex]
[tex]x = \frac{84}{\frac{53}{90}}[/tex]
[tex]x = \frac{84}{1} * \frac{90}{53} = \frac{7560}{53} = 142\frac{34}{53}[/tex] km
