Question 4
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It took Mike 5.625 hours to travel over pack ice from one town in the Arctic to another town 180 miles away. During the return journey, it took him 10 hours.

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

What was the speed of Mike's snowmobile?

Step 1 ：Let's denote the speed of the snowmobile as \(s\) (in miles per hour) and the speed of the pack ice as \(p\) (in miles per hour).

Step 2 ：For the first trip, the total speed was the sum of the speed of the snowmobile and the pack ice, and the time was 5.625 hours. So, we have the equation: \(s + p = \frac{180}{5.625}\).

Step 3 ：For the second trip, the total speed was the difference of the speed of the snowmobile and the pack ice, and the time was 10 hours. So, we have the equation: \(s - p = \frac{180}{10}\).

Step 4 ：We can solve these two equations to find the speed of the snowmobile.

Step 5 ：Setting up the equations, we get: \[eq1 = Eq(p + s, 32.0)\] \[eq2 = Eq(-p + s, 18.0)\]

Step 6 ：Solving the equations, we get: \[solution = \{p: 7.00000000000000, s: 25.0000000000000\}\]

Step 7 ：The solution to the system of equations gives the speed of the snowmobile as 25 miles per hour.

Step 8 ：Final Answer: The speed of Mike's snowmobile is \(\boxed{25}\) miles per hour.