maths problem

Let x m/min and y m/min (x > y) be the speed of both people : If they start at same position and run at same direction.
One will overlap the other in 2mins :
2x - 2y = 400 ... (1)If they start at same position and run at opposite direction, they will meet in 55s:
(55/60)x + (55/60)y = 400 ... (2)By(1) , y = x - 200 , sub. into (2) : (55/60) (x + x - 200) = 400
2x - 200 = 400*12/11
x - 100 = 2400/11
x = 3500/11
y = 3500/11 - 200 = 1300/11The speed of both people are 3500/11 m/min and 1300/11 m/min.

Let speeds of two men are p m/s and q m/s respectively and p > q.

If they start at same position and run at same direction, they will meet again when the faster man is 1 whole loop (i.e.400m) ahead the slower man.

That means the distance between two men is 400m in 2min.

So, we have

(p - q) x 2 x 60 = 400 ----- (1)


Moreover,
if they start at same the position and run at opposite direction, they will meet in 55sec.

That means the total distance travelled by two men is exactly 400m.

So, we have

(p + q) x 55 = 400 ---- (2)



After solving equation (1) & (2),

we get the speeds.