Math Help - jockey puzzle

Can anybody help with this problem?

lightning lady and stirling monarch set off from the same point on their circular training track, with their jockeys riding them in opposite directions. the first time they meet, lightning lady has run 500m. the next time they meet stirling monarch still has 200m to go before he finishes his first lap. how far is it around their track?

Let d = distance around their track.
Let L = speed of ligtning lady
Let S = speed of stirling monarch

When Ligthning Lady (LL) traveled 500m, SM traveled (d-500) m, and that is for the same time t1.
So,
t1 = 500/L = (d -500)/S
L = 500S /(d-500)

When LL continued and traveled [(d-500) +200]m, SM traveled (500 -200)m, and that is also in the same t2.
So,
t2 = [(d-500) +200] /L = (500-200) /S
(d-300)/L = 300/S
L = (d-300)S /300

L = L
500S /(d-500) = (d-300)S /300
Cross multiply,
500(300) = (d-500)(d-300)
150,000 = d^2 -1600d +150,000
0 = d^2 -1600d
0 = d -1600
d = 1600 meters ---------answer.