let

v = the speed of the plane with no wind

y = the speed of the wind

x = v + y the maximum speed of the plane when flying with the wind

d = 1720 mi the distance traveled in one direction

t1 = 5 hr the time of the travel against the wind

t2 = 4 hr the time of the travel with the wind

traveling with the wind

x*t2 = d

4x = 1720 divide both sides by 4

x = 430

traveling against the wind

(v - y)*t1 = d

(v - y)5 = 1720 divide both sides by 5

v - y = 344

by solving the system of equations

v - y = 344

v + y = 430 (since x = v + y and x = 430)

we find

v = 387 mph

y = 43 mph

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

the speed of the plane with no wind is 387 mph.