One day it began to snow exactly at noon at a heavy and steady rate. A snowplow left its garage at 1:00 P.M., and another one followed in its tracks at 2:00 P.M.:
a) At what time did the second snowplow crash into the first?
b) Could the crash have been avoided by dispatching the second snowplow at 3:00 P.M. instead?

eqn1 = D[h[t], t] == r;
eqn2 = D[x[t], t] == k/h[t];
soln1 = DSolve[{eqn1, h[0] == 0}, h[t], t];
neweqn2 = eqn2 /. soln1;
soln2 = DSolve[{neweqn2, x[1] == 0}, x[t], t];
newsoln2 = soln2 /. t -> T;
aux = Solve[newsoln2[[1, 1, 2]] == y[t], T, Reals][[1, 1, 2]]
eqn3 = D[y[t], t] == k/h[t];
soln3 = DSolve[{eqn1, h[T] == 0}, h[t], t];
neweqn3 = eqn3 /. soln3;
eqn4 = neweqn3 /. T -> aux
soln4 = DSolve[{eqn4, y[2] == 0}, y[t], t]

t-> e^((r/k)y)(2-(r/k)y)