Question: User: With draw and complete computation 1. When a small airplane flies with the wind, it can travel 450 miles in 3 hours. When the same airplane flies in the opposite direction against the wind, it takes 5 hours to fly the same distance. Find the average rate of the plane in still air and the average rate of the wind. 2. A chemist working on a flu vaccine needs to mix a 10% sodium iodide solution with a 60% sodium-iodine solution to obtain 50 milliliters of a 30% sodium-iodine solution. How many milliliters of the 10% solution and of the 60% solution should he mix? 3. Two towns, A and B, are 420 km apart. A bus leaves Town A toward Town B at 60 km/h. Two hours later, a car leaves Town B toward Town A at 90 km/h. At the moment the car starts, a motorcycle also leaves Town A toward Town B at 120 km/h. Determine: a. How long after the car starts will the bus and car meet? b. How far from Town A will they meet? c. Will the motorcycle reach the meeting point before or after the bus and car meet, and by how many minutes? 4. After designing your Web site, you and your friend decide to go into business setting up sites for others. With lots of practice, you can now work together and design a modest site in 4 hours. Your friend is still a faster worker. Working alone, you require 6 more hours than she does to design a site for a client. How many hours does it take your friend to design a Web site if she works alone? 5.A laboratory mixes 10% alcohol solution, 25% alcohol solution, and pure alcohol (100%). If equal amounts of the first two solutions are used and the final mixture is 40 liters at 35% alcohol, how many liters of pure alcohol were added?

1. Problem: Find the average rate of the plane in still air and the average rate of the wind given the airplane travels 450 miles with the wind in 3 hours and against the wind in 5 hours. 2. Formula and variables: Let $p$ = plane speed in still air (mph), $w$ = wind speed (mph). With wind: speed = $p + w$, time = 3 hours, distance = 450 miles. Against wind: speed = $p - w$, time = 5 hours, distance = 450 miles. 3. Set up equations from distance = speed \times time: $$450 = (p + w) \times 3$$ $$450 = (p - w) \times 5$$ 4. Simplify: $$p + w = \frac{450}{3} = 150$$ $$p - w = \frac{450}{5} = 90$$ 5. Add the two equations: $$ (p + w) + (p - w) = 150 + 90 $$ $$ 2p = 240 $$ $$ p = 120 $$ 6. Substitute $p=120$ into $p + w = 150$: $$ 120 + w = 150 $$ $$ w = 30 $$ 7. Final answer: The plane's speed in still air is $\boxed{120}$ mph. The wind speed is $\boxed{30}$ mph.