It took Todd 11 hours to travel over pack ice from one town in the Arctic to another town 330 miles away. During the return journey, it took him 15 hours.

Assume the pack ice was drifting at a constant rate, and that Todd’s snowmobile was traveling at a constant speed relative to the pack ice.

What was the speed of Todd's snowmobile?

To solve this problem, let's denote:

- \( v \) as the speed of Todd's snowmobile relative to the pack ice (in miles per hour).
- \( w \) as the speed of the pack ice (in miles per hour).

### Outward Journey:
- The effective speed of Todd's snowmobile relative to the ground during the outward journey (in the same direction as the pack ice) is \( v + w \).
- The time taken for the outward journey is 11 hours.
- The distance covered is 330 miles.

So, we can write the equation:
\[
v + w = \frac{330 \text{ miles}}{11 \text{ hours}} = 30 \text{ miles per hour}
\]

### Return Journey:
- The effective speed of Todd's snowmobile relative to the ground during the return journey (against the direction of the pack ice) is \( v - w \).
- The time taken for the return journey is 15 hours.
- The distance covered is 330 miles.

So, we can write the equation:
\[
v - w = \frac{330 \text{ miles}}{15 \text{ hours}} = 22 \text{ miles per hour}
\]

### Solving the System of Equations:
Now, we have two equations:
1. \( v + w = 30 \)
2. \( v - w = 22 \)

We can solve these equations by adding and subtracting them:

1. Add the two equations:
\[
(v + w) + (v - w) = 30 + 22
\]
\[
2v = 52
\]
\[
v = 26 \text{ miles per hour}
\]

2. Subtract the second equation from the first:
\[
(v + w) - (v - w) = 30 - 22
\]
\[
2w = 8
\]
\[
w = 4 \text{ miles per hour}
\]

### Conclusion:
The speed of Todd's snowmobile relative to the pack ice is \( v = 26 \) miles per hour.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How would the problem change if Todd traveled a different distance?
2. What if Todd's speed was not constant? How would that affect the calculation?
3. How could we determine the speed of the pack ice directly?
4. What would happen if the pack ice was drifting in the opposite direction on the return journey?
5. Could this problem be solved using vectors? How?

**Tip:** For problems involving relative motion, always identify the different reference frames and how velocities add or subtract depending on the direction.

It took Todd 11 hours to travel over pack ice from one town in the Arctic to another town 330 miles away. During the return journey, it took him 15 hours. Assume the pack ice was drifting at a constant rate, and that Todd’s snowmobile was traveling at a constant speed relative to the pack ice. What was the speed of Todd's snowmobile?

Solve the problem of calculating the speed of Todd's snowmobile as he travels over pack ice. This problem involves algebraic concepts, such as systems of equations and relative motion, making it suitable for students in Grades 9-10. Learn how to approach and solve this real-world problem step by step.

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