let

d = 280 mi the distance traveled in each direction

t1 = 1 hr 10 min = 1 + 10/60 = 1 + 1/6 = 7/6 hr traveling against the wind (since 1 hr = 60 min, 1 min = 1/60 hr)

t2 = 50 min = 50/60 hr = 5/6 hr traveling with the wind (since 1 hr = 60 min, 1 min = 1/60 hr)

w = the speed of the wind

v = the speed of the plane in still air

since speed = distance/time we have:

traveling against the wind the speed of the plane is: v - w

v - w = d/t1

v - w = 280/(7/6)

v - w = 240

traveling with the wind the speed of the plane is: v + w

v + w = d/t2

v + w = 280/(5/6)

v + w = 336

by solving the system of equations:

v - w = 240

v + w = 336

we find:

v = 288 mph

w = 48 mph

click here to see the step by step solution of the system of equations:

the speed of the wind is 48 mph.

the speed of the plane in still air is 288 mph.