История изменений

 resources :users, controller: 'public/users', only: [:new, :create]
  resources :users, controller: 'admin/users',  only: [:index, :destroy]
  resources :users, controller: 'user/users',   only: [:edit, :update, :show]

  resources :sessions, only: [:new, :create, :destroy]

  root to: "public/page#index"

  get    '/signup',   to: 'public/users#new',  as: 'signup'
  get    '/signin',   to: 'sessions#new',      as: 'signin'
  delete '/signout',  to: 'sessions#destroy',  as: 'signout'
  get    '/user/:id', to: 'user/users#edit',   as: 'show'
  get    '/users',    to: 'admin/users#index',
 
  resources :log_times, controller: 'admin/log_times', only: [:index, :new, :create, :destroy]
  resources :log_times, controller: 'user/log_times',  only: [:history, :show, :edit, :update]

namespace :admin do
    resources :log_times
  end

  namespace :user do
    resources :log_times
  end

Для контроллеров в пространстве имен можно использовать обозначение директории. Например:

resources :user_permissions, controller: 'admin/user_permissions'

 resources :users, controller: 'public/users', only: [:new, :create]
  resources :users, controller: 'admin/users',  only: [:index, :destroy]
  resources :users, controller: 'user/users',   only: [:edit, :update, :show]

  resources :sessions, only: [:new, :create, :destroy]

  root to: "public/page#index"

  get    '/signup',   to: 'public/users#new',  as: 'signup'
  get    '/signin',   to: 'sessions#new',      as: 'signin'
  delete '/signout',  to: 'sessions#destroy',  as: 'signout'
  get    '/user/:id', to: 'user/users#edit',   as: 'show'
  get    '/users',    to: 'admin/users#index',
 
  resources :log_times, controller: 'admin/log_times', only: [:index, :new, :create, :destroy]
  resources :log_times, controller: 'user/log_times',  only: [:history, :show, :edit, :update]

namespace :admin do
    resources :log_times
  end

  namespace :user do
    resources :log_times
  end