To find the length of each flight, we can use the formula: distance = speed x time.
Let's assume the length of the outbound flight (from the starting point to the destination) is x miles. Since the flight averages 460 miles per hour, the time taken for the outbound flight can be calculated as x/460 hours.
For the return flight, which averages 500 miles per hour due to the tailwind, the time taken can be calculated as x/500 hours.
The total flying time for both flights is given as 4 hours and 48 minutes, which can be converted to hours as 4 + 48/60 = 4.8 hours.
Using this information, we can set up the equation:
x/460 + x/500 = 4.8
To solve this equation, we can multiply through by the common denominator of 460 and 500, which is 230,000:
500x + 460x = 4.8 * 230,000
960x = 1,104,000
x = 1,104,000 / 960
x ≈ 1,150
Therefore, the outbound flight is approximately 1,150 miles long.
To find the duration of each flight, we can substitute this value back into the equations:
Outbound flight duration = 1,150 miles / 460 miles per hour ≈ 2.5 hours
Return flight duration = 1,150 miles / 500 miles per hour = 2.3 hours
Hence, the outbound flight lasts approximately 2 hours and 30 minutes, while the return flight lasts approximately 2 hours and 18 minutes.