100 POINTS Island Boat Trip
You are traveling to an island that is accessible only by boat. You plan to take one boat there and a different boat back. Determine how fast each boat travels. In this assignment, you may work alone, with a partner, or in a small group. Discuss the results of your work and/or any lingering questions with your teacher.
1
Circle the two boats you picked for your trip.

What do you know?
The steamboat makes the trip in 5 hours, the tall ship makes it in 10 hours, and that the tall ship is 10 knots slower than the steamboat.
What do you want to find out? How fast does each boat travel in knots?
What kind of answer do you expect? An equation?
Writing some expressions we can use the fact that the distance they will travel would be the same and that the trip time multiplied by the speed equals distance traveled.
3
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 points)
d=xT
4
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. (2 points)

5.
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. (2 points)

6.
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. (1 point)

7.
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)

8.
How fast does the second boat travel? Show your work. (2 points: 1 point for showing your work, 1 point for the answer)