Let

v1 = the speed of John

v2 = the speed of Tony

t1 = the walking time of John

t2 = the walking time of Tony

d = 10 miles the walking distance

v1 = 2*v2 (John walks twice as fast as Tony)

t2 = t1 + 3 (John arrives 3 hours before tony)

speed = distance / time

v1 = 10/t1 => t1 = 10/v1

v2 = 10/t2 => t2 = 10/v2

Thus we have the system of equations

v1 = 2*v2

10/v2 = 10/v1 + 3

by solving it

10/v2 = 10/(2*v2) + 3 multiply both sides by v2

10 = 5 + 3*v2

v2 = 5/3 mph = 1.67 mph approximately

v1 = 10/3 mph = 3.33 mph approximately

The speed of John is 1.67 mph approximately.

The speed of Tony is 3.33 mph approximately.