1. **Problem statement:** Find an expression in $x$ for $T$, the total time in hours, that it will take Jacob to kayak from $S$ to $B$ and then run from $B$ to $F$. 2. **Given:** - $|AB| = x$ km, where $0 \leq x \leq 8$. - Jacob kayaks from $S$ to $B$. - Jacob runs from $B$ to $F$. 3. **Step 1: Express distances** - The distance from $S$ to $B$ is the straight line distance. Since $S$ is 2 km from $A$ perpendicular to $AF$, the distance $SB = \sqrt{x^2 + 2^2} = \sqrt{x^2 + 4}$ km. - The distance from $B$ to $F$ is along $AF$, so $BF = 8 - x$ km. 4. **Step 2: Use speeds to find time** - Let the kayaking speed be 6 km/h. - Let the running speed be 12 km/h. 5. **Step 3: Write the total time $T$** $$ T = \text{time kayaking} + \text{time running} = \frac{\sqrt{x^2 + 4}}{6} + \frac{8 - x}{12} $$ 6. **Final expression:** $$ T(x) = \frac{\sqrt{x^2 + 4}}{6} + \frac{8 - x}{12} $$ This expression gives the total time in hours for Jacob to kayak from $S$ to $B$ and then run from $B$ to $F$ as a function of $x$.