A spy plane, whose average speed in still air is 250 mph, departs with a 40 mph tailwind
and returns to the same airport flying into the same wind. How far from the airport can
the plane fly if it has enough fuel to fly for 5 hours?
time there= distance/290
time back=distance/210
5hours=distance(1/290 + 1/210)
5=distance(210+290)/(210*290)
distance=5*(60900)/(500)=609 miles
To calculate the distance the spy plane can fly, we need to consider its speed with respect to the wind. Let's break down the problem step by step:
1. Find the speed of the plane with the tailwind:
The average speed of the plane in still air is given as 250 mph, and it has a 40 mph tailwind. So, the speed of the plane with the tailwind will be 250 mph + 40 mph = 290 mph.
2. Find the speed of the plane against the wind:
When the plane flies back to the airport, it is flying against the same 40 mph wind. Therefore, its speed against the wind will be 250 mph - 40 mph = 210 mph.
3. Calculate the distance the plane can cover with the tailwind:
Since the plane can fly for 5 hours, we can multiply the time by the speed of the plane with the tailwind: Distance = Speed × Time = 290 mph × 5 hours = 1450 miles.
4. Calculate the distance the plane can cover against the wind:
Using the same logic, we can calculate the distance the plane can cover when flying against the wind: Distance = Speed × Time = 210 mph × 5 hours = 1050 miles.
5. Determine the total distance from the airport that the plane can fly:
To determine the total distance, we need to consider the distance covered in both directions. Since the plane covers 1450 miles with the tailwind and 1050 miles against the wind, the total distance it can fly is 1450 miles + 1050 miles = 2500 miles.
Therefore, the spy plane can fly a maximum distance of 2500 miles from the airport if it has enough fuel to fly for 5 hours.