Since Tom must jog 1 lap (640 m) more than John before catching up,

then the problem is same as Tom starting off 1 lap (640m) behind John:

Code:

(640) John........@ a mpm.............>16 min
Tom.......................@ (160 - a) mpm.....................>16 min

Since they meet every 4 min if starting in different directions, then

combined speed is 640/4 = 160 mpm (meters per minutes):

then, let John's speed = a mpm: then Tom's speed = 160 - a mpm.

Using the basic speed = distance / time formula, then for Tom:

(16a + 640) / (160 - a) = 16

Solve to get a = 60 : so Tom's speed = 160 - 60 = 100 mpm.

So time for Tom to jog 1 lap = 640 / 100 = 6.4 min = 6 min 40 sec.