Code problem JQuery - password form -perfect

//hints shown always
//solution hide hints and show at apropriate times
var $password = $("#password");
var $confirmPassword = $("#confirm_password");

//hide hints
$("form span").hide();

function isPasswordValid() {
  return $password.val().lenght > 8;
}

function arePasswordsMatching() {
return $password.val() === $confirmPassword.val();
}

function canSubmit() {
return isPasswordValid() && arePasswordsMatching();
}

function passwordEvent() {
//find out if password is valid
if(isPasswordValid()) {
  //hide hint if valid
  $password.next().hide();
} else {
//else show hint

  $password.next().show();
  }
}

function confirmPasswordEvent() {
 if(arePasswordsMatching()) {
//hide hint if matched 
$confirmPassword.next().hide();
 } else {
 $confirmPassword.next().show();
   //else show hint 
 }
}

function enableSubmitEvent() {
$("#submit").prop("disabled", !canSubmit());
}

//when event happens on password input
$password.focus(passwordEvent).keyup(passwordEvent).keyup(confirmPasswordEvent).keyup(enableSubmitEvent);

$confirmPassword.focus(confirmPasswordEvent).keyup(confirmPasswordEvent).keyup(enableSubmitEvent);

enableSubmitEvent();
//when event happens on confirmation input
  //find out if password and confirmation match