A boat 4

A boat travels 25 km upstream in 5 hours and 25 km downstream in 2.5 hours. If the boat increased its speed by 3 km/h, it would take 1 hour less to travel the downstream distance. Find the speed of the stream.

Correct answer:

s =  2.5 km/h

Step-by-step explanation:

$$\begin{gathered} a=25\text{km} \\ {t}_1=5\text{h} \\ {t}_2=2.5\text{h} \\ a=(v-s)\cdot t_1 \\ a=(v+s)\cdot t_2 \\ 25=(v-s)\cdot 5 \\ 25=(v+s)\cdot 2.5 \\ 5s-5v=-25 \\ 2.5s+2.5v=25 \\ Row2-\frac{2.5}{5}\cdot Row1\to Row2 \\ 5s-5v=-25 \\ 5v=37.5 \\ v=\frac{37.5}{5}=7.5 \\ s=\frac{-25+5v}{5}=\frac{-25+5\cdot 7.5}{5}=2.5=2.5\text{km/h} \\ s=\frac{5}{2}=2.5 \\ v=\frac{15}{2}=7.5 \\ \text{ Verifying Solution: } \\ {t}_3=\frac{a}{v+3+s}=\frac{25}{7.5+3+2.5}=\frac{25}{13}\doteq 1.9231\text{h} \\ {t}_3=t_2-1 \end{gathered}$$

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