Question: Solving equations based on numeric solution of ODE

Dear Maple users

Some ODE's like the Lotka Volterra system can only be solved numerically. I would like to solve some equations based on the numerical solution to that system. Let the x(t) and y(t) be the solutions to the ODE system. 

Now, obviously it won't work afterwards to write an equation like solve(x(t)=60,t), since the solution of the ODE only exists as a procedure. Of course I can make an odeplot and zoom in to get an approximate solution to x(t)=60. I would however like it to done automatically. How is this done in the most convenient way when the soltuion of the ODE is given as a procedure?

Example attached. 



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