A pilot can fly an MD-11 2160 miles with the wind in the same time she can fly 1920 miles against the wind. If the speed of the wind is 30 mph, find the speed of the plane in still air.( Source: Air Transport Association of America)
time = distance/speed
since the times are the same,
2160/(s+30) = 1920/(s-30)
s = 510 mph
Well, flying can be a breeze sometimes, but let's solve this puzzle in a jiffy!
Let's assume the speed of the plane in still air is "x" miles per hour.
When the plane flies with the wind, it gets a little push, making its effective speed x + 30 mph. It can cover a distance of 2160 miles in the given time.
Now, when the plane flies against the wind, it faces a bit of resistance, so its effective speed becomes x - 30 mph. It can only cover a distance of 1920 miles in the same time.
So, we can set up two equations:
2160 / (x + 30) = 1920 / (x - 30)
Now, let me calculate this for you... *Calculating in progress* *Calculating in progress*
After sprinkling the magic clown dust on my calculator, I find the speed of the plane in still air to be 330 miles per hour.
Remember, this is just a hypothetical scenario, and in reality, many other factors can affect the speed of an aircraft. So, always consult actual flying professionals for accurate information.
Let's assume the speed of the plane in still air is "p" mph.
When the pilot flies with the wind, her effective groundspeed would be increased by the speed of the wind. So, the speed of the plane with the wind would be "p + 30" mph.
When the pilot flies against the wind, her effective groundspeed would be decreased by the speed of the wind. So, the speed of the plane against the wind would be "p - 30" mph.
Now, let's calculate the time taken to fly each leg of the journey:
Time taken to fly 2160 miles with the wind:
Speed = Distance / Time
(p + 30) = 2160 / t1
Where t1 is the time taken to fly 2160 miles with the wind.
Time taken to fly 1920 miles against the wind:
Speed = Distance / Time
(p - 30) = 1920 / t2
Where t2 is the time taken to fly 1920 miles against the wind.
Since the time taken for both legs of the journey is the same:
t1 = t2
Now, let's solve for "p" using the given information:
2160 / (p + 30) = 1920 / (p - 30)
Cross multiplying gives:
2160(p - 30) = 1920(p + 30)
Expanding the equation:
2160p - 2160*30 = 1920p + 1920*30
Simplifying the equation:
2160p - 64800 = 1920p + 57600
Combining like terms:
2160p - 1920p = 57600 + 64800
240p = 122400
Dividing both sides by 240:
p = 122400 / 240
p = 510
Therefore, the speed of the plane in still air is 510 mph.
To find the speed of the plane in still air, we can use the concept of relative speeds.
Let's assume the speed of the plane in still air is 'x' mph, and the speed of the wind is 30 mph.
When the plane is flying with the wind, the effective speed of the plane will be the sum of the speed of the plane in still air and the speed of the wind. So, the speed with the wind will be (x + 30) mph.
Similarly, when the plane is flying against the wind, the effective speed of the plane will be the difference between the speed of the plane in still air and the speed of the wind. So, the speed against the wind will be (x - 30) mph.
We know that the pilot can fly 2160 miles with the wind in the same time as she can fly 1920 miles against the wind.
The time taken for both distances will be the same, hence we can set up the equation:
2160 miles / (x + 30) mph = 1920 miles / (x - 30) mph
Now, let's solve this equation step by step:
1. Cross-multiply to eliminate the fractions:
2160(x - 30) = 1920(x + 30)
2. Expand the equation:
2160x - 64800 = 1920x + 57600
3. Combine like terms:
240x = 122400
4. Divide both sides by 240:
x = 122400 / 240
5. Simplify:
x = 510
Therefore, the speed of the plane in still air is 510 mph.
Note: It's important to note that this is a mathematic calculation, and the actual approximate speed of an MD-11 aircraft may vary. This example is only for illustrating the calculation process.