halfway to hawaii

Anyone that has flown United Airlines to Hawaii should be familiar with the contest on board. Each passenger is asked to submit a guess of when the flight will be halfway to Hawaii. I figured with a calculator or lap top computer, I would be able to win each year. I started asking pilots on how to work out the calculations. Each flight, I took I never won. Finally I figured it out and here is the answer so you can do the same.

official rules

"Aloha and welcome to United Airlines. We invite you to participate in our game of determining the exact time we will reach the geographical midpoint between the Mainland and Hawaii."

formulas

Ground Speed = True Airspeed + Tail Wind
Ground Speed = True Airspeed - Head Wind

(.5 * total miles) / First Leg Ground Speed = X
(.5 * total miles) / Second Leg Ground Speed = Y
Convert X and Y to time. The numbers to the left of the decimal point are the hours. The numbers to the right of the decimal point is the portion of the hour. Multiple the number to the right of the decimal point by 60 to get the number of minutes.
X + Y = TOTAL TIME
EXAMPLE:
(.5 * 2184) / (466 + 5) = 2.3184713375796178343949044585987 or 2 h (0.31847133757961783439490445859873 * 60) 19 m = 2 h 19 m

information provided

At the beginning of the flight the pilot will provide you with the following information. I have also provided the official answers for you to try and work out the formula.

flight one

2184 nautical miles
4:57 total time
8:23am departure
--> 5:23am Maui time at departure
Use Hawaiian time for answer
466 knots the first half of trip
467 knots the second half of trip
5 knots tailwind the first half
3 knots headwind the second half

Answer: 07:42:37

flight two

2078 nautical miles
4:44 total time
9:41am departure
--> 6:41am Maui time at departure
Use Hawaiian time for answer
462 knots the first half of trip
465 knots the second half of trip
5 knots tailwind the first half
11 knots headwind the second half

Answer: 11:52:16

answer

If you did the math, the numbers don't match. The key is the 'actual' midpoint. The pilot gave some information that would be helpful if the plane actually went that speed.The key word is 'actual'. The pilot gives you bunch of numbers that you can use to figure out the "estimated" time. If the pilot does not actually travel those speeds, which he/she never does, the numbers will be off.

If I told you that I was going to drive 60 miles and I was going to drive 60 miles per hour and I was leaving at 9:00 you should be able to tell me when I got to geographical midpoint. The problem is that I won't always drive 60 miles per hour. I may get stuck in traffic and slow down to 25 or go down a hill at 75. When my odometer hits 30 miles, I can look at my clock and find the actual time.

The only part that is fixed is what time the plane left. The total flying time is usually accurate as well. The speed that the plane is traveling may be faster or slower than what the pilot said. The key is to GUESS! Divide the total flying time by two (2). Add some time if the plane is slower on the first half, subtract time if the plane is faster in the first half.

GOOD LUCK!