Can someone solve this arithmetic problem for me?

The total distance to be flown is 2850 miles in six hours.

3,5 hours have been travelled at 436 mph, so a distance of 1526 has been travelled (3,5 hours * 436 miles per hour)

The journey may last 6 hours, so their is 2,5 hours left (6 hours to go – 3.5 hours travelled)

In those 2.5 hours 1324 miles will have to be travveled (2850 miles to go – 1526 miles traveled)

The speed needed for that is 529.6 mph (1324miles / 2,5 hours)

So the answer is 529.6 mph

436mph x 3.5 h = 1526 m travelled
2850–1526 = 1324 m to go with 2.5 h left
1324 m / 2.5 h = 529.6 mph

The answer provided above is the way I see it as well. I think you are reading too much into “good speed”. They did not pose the question as“the plane was traveling at a speed of 500 mph without wind effect, but in fact faced a head wind of 20 mph. What would the actual speed of the plane be and what would the speed need to be if they then experienced a tail wind of 15 mph for the balance of the flight?” So again, I believe you were given the correct answer by my esteemed colleagues. See ya….Gary/wtf
PS: Welcome to fluther.

Thanks guys :).