APEX ANSWERS PLEASE HELP
1.9.6 Practice: Modeling: Multistep Linear Equations

1 Circle the two boats you picked for your trip, and explain why you selected them. (3 points: 1 point for each selection, 1 point for your explanation)

2 I chose these boats because:

3. Take what you know about traveling to and from the island by boat and write it as a sentence. (2 points)

4. Let x be the speed of the boat you are taking to the island. The other boat's speed can then be written relative to the variable x. Write the speed of each boat using the variable x. (2 points: 1 point for each boat)

5. Each ship travels the same distance. Remember that the trip time multiplied by the speed equals the 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)

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

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

8. If the yacht trip costs $75, the tall ship trip costs $25, and the steamboat trip costs $40, how much does each trip cost per hour? (1 point)

1. For this problem I found the details of the ships in another source. Let us use the steamboat for going to the island and then switch to the tall ship when going back. We know that 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.

2. We'll actually be good with whatever we choose but we just chose those two aforementioned boats because they will be the two most appropriate and inexpensive boats that can safely transport you back and forth the island. The details of the two boats have also been given for us to analyze.

3. As previously stated, travelling to the island would take us 5 hours while going back would take us 10 hours. We also know that the tall ship is 10 knots slower than the steamboat however we do not know the actual speed of any boat. Luckily, 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.

4. For this item we just assign the variable x as the speed of the steamboat and use the fact that the tall boat is 10 knots slower than the steamboat to write its speed in terms of the variable x. With this information, we can find out that the tall boat's speed is (x-10) knots.

Speed of the steamboat: x knots
Speed of the tall boat: (x-10) knots

5. Since we know the trip time and we have already designated variables for the speed, we will just multiply these two to find out the distance. Given that the distance traveled for both boats is the same, we will just equate the expressions for both boats.

[tex]5x=10(x-10)[/tex]

6. [tex]5x=10(x-10)[/tex]
[tex]5x=10x-100[/tex]
[tex]100=5x[/tex]
[tex]x=20[/tex]

Based on our calculations, the value for x is 20. This would tell us that the speed of the steamboat (which we designated as x earlier) is equal to 20 knots.

7. Since we designated the second boat (tall boat) to have a speed of (x-10) knots, we just use the value of x that we got in the previous item and subtract 10 from it.

Speed of the tall boat: [tex]x-10=20-10=10[/tex] knots

8. For this item, we are only asked to provide the cost per hour for the boats we've picked. We already know the trip time of the two boats (as mentioned before) and we are already given the costs for each one therefore we just divide the two units to compute for the cost per hour.

Steamboat: [tex] \frac{40dollars}{5hours}=8dollars/hour[/tex]
Tall boat: [tex] \frac{25dollars}{10hours}=2.5dollars/hour[/tex]