Answer: the speed of the plane is 7.4 miles per minute.
the speed of the wind is 0.93 miles per minute.
Step-by-step explanation:
Let x represent the speed of the plane.
Let y represent the speed of the wind.
Distance of Las Cruses, NM from Dallas, TX is 600 miles.
Distance = speed × time
One plane flies from Dallas to Las Cruses in 1 hr 12 min(72 minutes). Assuming the plane flew in the same direction with the wind, then
600 = 72(x + y)
600 = 72x + 72y - - - - - - - - 1
Another plane with the same air speed flies from Las Cruses to Dallas in 1 hr 30 min(90 minutes). Assuming it flew in opposite direction to that of the wind, then
600 = 90x - 90y - - - - - - - 2
Adding equation 1 and equation 2, it becomes. 1200 = 162x
x = 1200/162 = 7.4 miles per minute.
x + y = 600/72 = 8.33
y = 8.33 - x = 8.33 - 7.4 = 0.93 miles per minute
