A man flies a small airplane from Fargo to Bismarck, North Dakota -- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 12 minutes. What is his speed in still air, and how fast is the wind blowing? Give both answers in $\mathrm{mph}$.
Your answer is
his speed equals
the wind speed equals

Step 1 ：Let's denote the speed of the plane in still air as 'p' (in mph) and the speed of the wind as 'w' (in mph).

Step 2 ：When the man is flying against the wind (from Fargo to Bismarck), his effective speed is (p - w) mph. Given that the distance is 180 miles and the time taken is 2 hours, we can set up the equation: \(180 = 2 * (p - w)\)

Step 3 ：When the man is flying with the wind (from Bismarck to Fargo), his effective speed is (p + w) mph. Given that the distance is again 180 miles and the time taken is 1 hour 12 minutes (or 1.2 hours), we can set up the equation: \(180 = 1.2 * (p + w)\)

Step 4 ：We can solve these two equations simultaneously to find the values of 'p' and 'w'.

Step 5 ：Final Answer: The speed of the plane in still air is \(\boxed{120}\) mph and the speed of the wind is \(\boxed{30}\) mph.