Положите что-то вроде
[[NSUserDefaults standardUserDefaults] setObject:[NSDate date] forKey:@"kLastCloseDate"];
в оба
- (void)applicationWillTerminate:(UIApplication *)application
- (void)applicationDidEnterBackground:(UIApplication *)application
Затем проверьте разницу при запуске:
NSDate *lastDate = [[NSUserDefaults standardUserDefaults] objectForKey:@"kLastCloseDate"];
NSTimeInterval timeDiff = [[NSDate date] timeIntervalSinceDate:lastDate];
// your stuff
в обоих
- (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions
- (void)applicationWillEnterForeground:(UIApplication *)application