Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 974

\[x\ км\text{/}ч - собственная\ скорость\ \]

\[катера;\]

\[\text{y\ }км\text{/}ч - скорость\ течения\ реки.\]

\[1)\ \frac{30}{x + y} + \frac{20}{x - y} = \frac{10}{y}\ \ \ \ \ | \bullet y\left( x^{2} - y^{2} \right)\]

\[30y(x - y) + 20y(x + y) =\]

\[= 10\left( x^{2} - y^{2} \right)\]

\[30xy - 30y^{2} + 20xy + 20y^{2} =\]

\[= 10x^{2} - 10y^{2}\]

\[10x^{2} = 50xy\]

\[x^{2} = 5xy\]

\[x = 5y.\]

\[2)\ \frac{36}{x + y} + 10 = \frac{36}{y}\]

\[\frac{36}{5y + y} + 10 = \frac{36}{y}\]

\[\frac{36}{6y} + 10 = \frac{36}{y}\]

\[\frac{6}{y} + 10 = \frac{36}{y}\]

\[\frac{30}{y} = 10\]

\[10y = 30\]

\[y = 3;\]

\[x = 5 \bullet 3 = 15.\]

\[Ответ:\ \ 15\ км\text{/}ч.\]