1. **State the problem:** A boat travels 25 km upstream in 5 hours and returns downstream in 0.5 hours. We need to find the speed of the boat in still water ($b$) and the speed of the current ($c$). 2. **Define variables and formulas:** - Speed upstream = $b - c$ - Speed downstream = $b + c$ Using the formula for speed: $$\text{speed} = \frac{\text{distance}}{\text{time}}$$ 3. **Write equations from the problem:** - Upstream speed: $$b - c = \frac{25}{5} = 5$$ - Downstream speed: $$b + c = \frac{25}{0.5} = 50$$ 4. **Solve the system of equations:** Add the two equations: $$ (b - c) + (b + c) = 5 + 50 $$ $$ 2b = 55 $$ $$ b = \frac{55}{2} = 27.5 $$ Subtract the first equation from the second: $$ (b + c) - (b - c) = 50 - 5 $$ $$ 2c = 45 $$ $$ c = \frac{45}{2} = 22.5 $$ 5. **Final answer:** - Speed of the boat in still water is $27.5$ km/h. - Speed of the current is $22.5$ km/h.