Problem

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.

Solution

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.

From Solvely APP
Source: https://solvelyapp.com/problems/GjTQmcuGOT/

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