2.1.4Practice: Modeling: Multistep Linear Equations Practice

Algebra I Honors

Points Possible:30

Name:

Parker Howell

Date:

YOUR ASSIGNMENT: 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.

2.

Writing some expressions
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)

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)

9. When you get to the island, you decide to take a kayak tour to a nearby reef. A kayak is a small boat you row with a paddle.
Find the speed for the kayak. Use one of these facts to help.
The steamboat's speed is 4 less than 8 times the speed of the kayak.
The tall ship's speed is 1 more than 3 times the speed of the kayak.
The yacht's speed is 5 less than 15 times the speed of the kayak.
Write and solve an equation for the speed of the kayak. Show your work. (5 points: 2 points for writing a correct equation, 3 points for the solution)

10. The length of your trip to the island is 40 nautical miles less than 20 times the distance to the reef.
It's 2:00 p. m. now, and your boat leaves the island at 7:30 p. m. Will you be able to kayak to the reef and back by then?
If so, how long will you have to spend at the reef?
If not, how late will you be for the return trip?
Explain how you plan to solve this problem. Then solve the problem, showing all work. (5 points: 2 points for the explanation of the plan, 1 point for deciding if you will make it back to the island on time, and 2 points for determining either how long you can spend at the reef or how late you'll be)