let

v = jet's speed in still air

w = 18 mph the wind speed

d1 = 852 mi the distance of the flight with tale wind

d2 = 1560 mi the distance of the flight against the wind

t = the time of the flight against the wind

t/2 = the time of the flight with tail wind

flying with tale wind the speed of the plane is: v + w = v + 18

v + 18 = d1/(t/2)

v + 18 = 852/(t/2)

v + 18 = 2*852/t

t = 2*852/(v + 18)

fling against the wind the speed of the plane is: v - w = v - 18

v - 18 = d2/t

v - 18 = 1560/t

plug t = 2*852/(v + 18) into the last equation

v - 18 = 1560/(2*852/(v + 18))

by solving we find:

v = 408 mph

click here to see the step by step solution of the equation:

the jet's speed is 408 mph.