question_answer

            Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.

Answer:

Let speed of stream be x

according to question,

\[\frac{30}{x+15}+\frac{30}{15-x}=4+\frac{30}{60}\]

\[30\frac{(15-x+x+15)}{{{(15)}^{2}}-{{(x)}^{2}}}=\frac{9}{2}\]

\[\frac{900}{225-{{x}^{2}}}=\frac{9}{2}\]

\[\Rightarrow \]                  \[\frac{2}{9}\times 900=225-{{x}^{2}}\]

\[200=225-{{x}^{2}}\]

or                            \[-{{x}^{2}}=200-225=-25\]

or                                \[x=5\,\,km/hr.\]

Speed of stream is \[=5\,\,km/hr.\]