A = 0.01
B = 0.00001
eq1 = h'[t] == -A *h[t]* z[t]*r[t]
eq2 = z'[t] == A *h[t]*z[t] - B *h[t]*z[t]
eq3 = r'[t] == B *h[t] *z[t]
% sol = First[
h /. NDSolve[{eq1, eq2, eq3, h[0] == 1000000, z[0] == 1,
r[0] == 0}, {h, r, z}, {t, 0, 20}]]
sol = First[
h /. NDSolve[{eq1, eq2, eq3, h[0] == 99.9, z[0] == 0.1,
r[0] == 0}, {h, r, z}, {t, 0, 20}]]
sol2 = First[
z /. NDSolve[{eq1, eq2, eq3, h[0] == 99.9, z[0] == 0.1,
r[0] == 0}, {h, r, z}, {t, 0, 20}]]
I put the text above in and got three interpolating functions out. I need to solve for t when the first interpolating function is equal to 0.