1. **Stating the problem:** We have three cruisers A, B, and C spotted at the same area in the sea. We need to find: a. The distance from the pier where all three cruisers were spotted at the same time. b. Identify if each cruiser’s distance pattern is growing or shrinking and explain. c. Write the equation of each cruiser’s distance from the pier as a function of time in the form $y = mx + b$. d. Determine which cruiser(s) is/are travelling out into the sea. e. Find which cruiser has the greatest average speed and what that speed is. 2. **Analyzing the graph data:** - All three cruisers start at the same distance from the pier at time $x=0$, which is $y=200$ km. - Cruiser A increases from 200 km at $x=0$ to about 380 km at $x=5$. - Cruiser B increases from 200 km at $x=0$ to about 300 km at $x=5$. - Cruiser C decreases from 200 km at $x=0$ to about 0 km at $x=5$. 3. **Finding the distance where all cruisers were spotted at the same time:** Since all start at $x=0$ and $y=200$, the distance is $\boxed{200}$ km. 4. **Identifying growth or shrinkage:** - Cruiser A: Distance increases from 200 to 380 km, so it is **growing** (moving away from the pier). - Cruiser B: Distance increases from 200 to 300 km, so it is **growing** (moving away from the pier). - Cruiser C: Distance decreases from 200 to 0 km, so it is **shrinking** (moving toward the pier). 5. **Writing equations $y = mx + b$ for each cruiser:** - For all, $b = 200$ (initial distance at $x=0$). - Slope $m$ is change in distance over change in time. For Cruiser A: $$m = \frac{380 - 200}{5 - 0} = \frac{180}{5} = 36$$ Equation: $$y = 36x + 200$$ For Cruiser B: $$m = \frac{300 - 200}{5 - 0} = \frac{100}{5} = 20$$ Equation: $$y = 20x + 200$$ For Cruiser C: $$m = \frac{0 - 200}{5 - 0} = \frac{-200}{5} = -40$$ Equation: $$y = -40x + 200$$ 6. **Which cruiser(s) is/are travelling out into the sea?** Cruisers A and B have positive slopes, so they are travelling out into the sea. Cruiser C has a negative slope, so it is moving back toward the pier. 7. **Greatest average speed:** Speed is the absolute value of the slope $m$. - Cruiser A: 36 km/h - Cruiser B: 20 km/h - Cruiser C: 40 km/h Cruiser C has the greatest speed of 40 km/h but is moving toward the pier. Among those moving out, Cruiser A has the greatest speed of 36 km/h. **Final answers:** a. Distance where all spotted: $200$ km b. A and B growing (moving away), C shrinking (moving toward pier) c. Equations: - A: $y = 36x + 200$ - B: $y = 20x + 200$ - C: $y = -40x + 200$ d. Cruisers A and B travelling out into the sea e. Greatest average speed is Cruiser C at 40 km/h (toward pier), among those going out Cruiser A at 36 km/h