An airplane travels 4050 miles in 4.5 hours with the aid of a tail wind. It takes 5 hours for the return trip, flying against the same wind. Find the speed of the airplane in the still wind, and the speed of the wind.
Answers (1)
a = speed of the aircraft
b = speed of the breeze
On the journey there the two speeds add up to
[1]: a + b = 4050 / 4.5 = 900 mph
On the way back the aircraft has the opposite direction, so we'll have to subtract b from a
[2]: a - b = 4050 / 5 = 810 mph
We have to solve this system of two equations
[3]:=[1]-[2]: 2b = 90 mph
[4]: b = 45 mph
The speed of the wind is 45 mph.
[5]:=[1]<-[4]: a + 45 = 900 mph
[6]: a = 855 mph
[7]:=[2]<-[4]: a - 45 = 810 mph
[8]: a = 855 mph
The speed of the aircraft is 855 mph.