A plane completes a trip between two airports in 3 hours. The return trip between the same two airports, 50 mph faster with the help of wind, takes 2 3/4 hours. How far apart are the two airports?

Answer 1

Consider the velocity of the plane as v (in mph). Using the basic equation Distance = velocity x time, we can say about the first trip that the distance between the cities = (v) x (3 hrs). On the return trip, the velocity of the plane was v + 50. We can say the distance between the cities was (v + 50) x (2.75 hrs). But the distance between the cities is the same on the first trip and the second, so (v) x (3 hrs) = (v + 50) x (2.75 hrs):

3v = (v+50)2.75

3v = 2.75v + 137.5

0.25v = 137.5

v = 550 mph

so, d (in miles) = 550 mph x 3 hrs = 1650 miles