1. **State the problem:** A boat travels 336 miles downstream and back upstream. The downstream trip takes 12 hours, and the upstream trip takes 14 hours. We need to find the speed of the boat in still water ($x$) and the speed of the current ($y$). 2. **Define variables:** - Let $x$ = speed of the boat in still water (miles per hour). - Let $y$ = speed of the current (miles per hour). 3. **Write the equations:** - Downstream speed = $x + y$ - Upstream speed = $x - y$ 4. **Use the formula for speed:** $$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$ 5. **Set up equations from the problem:** - Downstream: $$x + y = \frac{336}{12} = 28$$ - Upstream: $$x - y = \frac{336}{14} = 24$$ 6. **Solve the system of equations:** Add the two equations: $$\begin{aligned} (x + y) + (x - y) &= 28 + 24 \\ 2x &= 52 \\ x &= \frac{52}{2} = 26 \end{aligned}$$ 7. **Find $y$ by substituting $x=26$ into one equation:** $$\begin{aligned} 26 + y &= 28 \\ y &= 28 - 26 = 2 \end{aligned}$$ 8. **Final answer:** - Speed of the boat in still water is $\boxed{26}$ miles per hour. - Speed of the current is $\boxed{2}$ miles per hour.