You are traveling to an island that is accessible only by boat. You plan to take a steamboat there and a yacht back. The steamboat makes the trip in 5 hours. The yacht makes the trip in 2.5 hours. The yacht is 20 knots faster than the steamboat. For each boat, the trip time multiplied by the speed equals the distance traveled. You know both boats will travel the same distance. How fast is each boat traveling in knots (nautical miles per hour)?

1. Write an expression for the distance going to the island. Let x be the speed of the boat you are taking to the island. Distance is equal to speed times time.

2. Write an expression for the speed of the boat coming back from the island in terms of the other boat's speed. Let x be the speed of the boat you are taking to the island.

3. Write an expression for the distance returning from the island. Use the expression for speed you found in question 4. Remember that distance is equal to speed times time.

4. Each ship travels the same distance. Set the distances equal to each other to get the equation for the speed of the ship you are taking to the island.

5. Solve the equation from question 6 for x. What does this tell you? (5 points: 1 point for showing your work, 3 points for solving for x, 1 point for explaining the answer)

6. How fast does the second boat travel? Show your work.