ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 807

\[\boxed{\text{807.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[S_{1} = 12,5\ км,\ \ S_{2} = 18\ км,\ \ \]

\[S_{3} = 14\ км\]

\[v_{1} = v_{2} - 1,\ \ v_{3} = v_{2} - 2,\ \ \]

\[t_{3} - t_{2} = 30\ мин = \frac{1}{2}ч\]

\[t_{3} = \frac{S_{3}}{v_{3}} = \frac{14}{v_{2} - 2},\ \ \]

\[t_{2} = \frac{S_{2}}{v_{2}} = \frac{18}{v_{2}}\]

\[\frac{14}{v_{2} - 2} - \frac{18}{v_{2}} = \frac{1}{2}\text{\ \ \ \ \ }\]

\[\ \ | \cdot 2v_{2}\left( v_{2} - 2 \right)\]

\[28v_{2} - 36 \cdot \left( v_{2} - 2 \right) =\]

\[= v_{2} \cdot \left( v_{2} - 2 \right)\]

\[28v_{2} - 36v_{2} + 72 - v_{2}^{2} +\]

\[+ 2v_{2} = 0\]

\[v_{2}^{2} + 6v_{2} - 72 = 0\]

\[D = 36 + 288 = 324 = 18^{2}\]

\[v_{1,2} = \frac{- 6 \pm 18}{2} = 6;\]

\[- 12 < 0 - не\ подходит\]

\[t_{1} = \frac{12,5}{6 - 1} = \frac{12,5}{5} =\]

\[= 2,5\ (ч) - занял\ первый\ \]

\[переход.\]

\[t_{2} = \frac{18}{6} = 3\ (ч) - второй\]

\[\ переход.\]

\[t_{3} = \frac{14}{6 - 2} = \frac{14}{4} = \frac{7}{2} =\]

\[= 3,5\ (ч) - третий\ переход.\]

\[Ответ:2,5\ ч;3\ ч;3,5\ ч.\ \]