An airplane flies 6300 miles into the wind for 18 hours. The return trip takes 14 hours. Find the speed of the airplane without a wind and the speed of the wind.
Answer
Final Answer: The speed of the airplane without wind is \(\boxed{400}\) miles per hour and the speed of the wind is \(\boxed{50}\) miles per hour.
Step 1 ：Let's denote the speed of the airplane as 'a' and the speed of the wind as 'w'.
Step 2 ：From the problem, we have the following two equations: \(a - w = \frac{6300}{18}\) and \(a + w = \frac{6300}{14}\).
Step 3 ：We can solve these two equations to find the values of 'a' and 'w'.
Step 4 ：The solution to the system of equations gives the speed of the airplane as 400 miles per hour and the speed of the wind as 50 miles per hour.
Step 5 ：This means that the airplane flies at a speed of 400 miles per hour when there is no wind, and the speed of the wind is 50 miles per hour.
Step 6 ：Final Answer: The speed of the airplane without wind is \(\boxed{400}\) miles per hour and the speed of the wind is \(\boxed{50}\) miles per hour.
