the plane travels with the wind at an average speed of 529 miles per hour and returns against the wind at an average speed of 408 miles per hour what is the distance it travels
no idea - how long did it fly?
To find the distance the plane travels, we need to know the time it takes to travel in each direction.
Let's assume the distance the plane travels is 'd' miles and the speed of the wind is 'w' miles per hour.
When the plane flies with the wind, its effective speed is (529 + w) miles per hour.
When the plane flies against the wind, its effective speed is (529 - w) miles per hour.
We can use the formula: Speed = Distance / Time to find the time it takes for the plane to travel in each direction.
For the plane traveling with the wind:
(529 + w) = d / t1
Solving for t1, we get t1 = d / (529 + w)
For the plane traveling against the wind:
(529 - w) = d / t2
Solving for t2, we get t2 = d / (529 - w)
Now, let's assume the plane takes 't' hours to travel one-way, meaning it takes '2t' hours for the round trip.
The total distance traveled during the round trip is the sum of the distances traveled in each direction:
Distance with the wind = Speed with the wind * Time = (529 + w) * t
Distance against the wind = Speed against the wind * Time = (529 - w) * t
Total distance traveled = Distance with the wind + Distance against the wind = (529 + w) * t + (529 - w) * t = 2 * 529 * t
Since we know the average speed while traveling with the wind is 529 miles per hour and against the wind is 408 miles per hour, we can calculate the time it takes for the round trip:
2 * 529 * t = 408 * 2t
Simplifying, we get:
1058t = 816t
Dividing both sides by t, we get:
1058 = 816
This equation is not true, which means there is no solution. Therefore, the question is not possible to answer with the given information.
Please note that this problem assumes a constant wind speed throughout the flight and neglects any other factors that may affect the travel time or distance.