A Coast Guard plane has enough fuel to fly for 6hr, and it's speed in still air is 240 mph. The plane departs with 40 mph tailwind and returns to the same airport flying into the wind. How far can the plane travel under these conditions?
Assuming the distance is x miles.
Then
with tail wind, ground speed=240+40=280 mph
against wind, ground speed = 240-40=200
Total time
x/280 + x/240 = 6
Solve for x to get the maximum one-way distance.
129.23 mph ...
To find the distance the Coast Guard plane can travel under these conditions, we need to calculate the time it will take the plane to fly with the tailwind and against the wind.
Given:
Time taken to fly with tailwind = 6 hours
Speed of the plane in still air = 240 mph
Tailwind speed = 40 mph
To calculate the time taken to fly with the tailwind, we can assume that the speed of the plane is the sum of its speed in still air and the tailwind speed. So:
Speed of the plane with tailwind = Speed in still air + Tailwind speed
Speed of the plane with tailwind = 240 mph + 40 mph = 280 mph
The distance traveled with the tailwind can be calculated by multiplying the time taken with the tailwind by the speed of the plane with the tailwind. So:
Distance traveled with tailwind = Time with tailwind × Speed with tailwind
Distance traveled with tailwind = 6 hours × 280 mph = 1680 miles
Next, let's calculate the time taken to fly against the wind. We can assume that the speed of the plane against the wind is the difference between its speed in still air and the tailwind speed. So:
Speed of the plane against the wind = Speed in still air - Tailwind speed
Speed of the plane against the wind = 240 mph - 40 mph = 200 mph
The time taken to fly against the wind can be calculated by dividing the total fuel time (6 hours) by the time for each leg of the journey (with the tailwind and against the wind combined). So:
Time taken to fly against the wind = Total fuel time / (Time with tailwind + Time against the wind)
Time taken to fly against the wind = 6 hours / 2 = 3 hours
Finally, to find the total distance traveled, we sum the distances traveled with the tailwind and against the wind. So:
Total distance traveled = Distance with tailwind + Distance against the wind
Total distance traveled = 1680 miles + (200 mph × 3 hours) = 1680 miles + 600 miles = 2280 miles
Therefore, under these conditions, the Coast Guard plane can travel a total distance of 2280 miles.