Add Login.PromptToLoginTime UMA metric

chrome/browser/chromeos/login/existing_user_controller.cc

Index: chrome/browser/chromeos/login/existing_user_controller.cc
diff --git a/chrome/browser/chromeos/login/existing_user_controller.cc b/chrome/browser/chromeos/login/existing_user_controller.cc
index c24adb98a5d5c9437de72c4abe6193d015ea3ea6..9a051eda58514c4bf1478935f02f9e1335c4bf70 100644
--- a/chrome/browser/chromeos/login/existing_user_controller.cc
+++ b/chrome/browser/chromeos/login/existing_user_controller.cc
@@ -517,6 +517,11 @@ void ExistingUserController::PerformLogin(
   }
   SendAccessibilityAlert(
       l10n_util::GetStringUTF8(IDS_CHROMEOS_ACC_LOGIN_SIGNING_IN));
+  if (!time_init_.is_null()) {
+    base::TimeDelta delta = base::Time::Now() - time_init_;
+    UMA_HISTOGRAM_MEDIUM_TIMES("Login.PromptToLoginTime", delta);
+    time_init_ = base::Time();  // Reset to null.
+  }
 }
 
 void ExistingUserController::ContinuePerformLogin(