The alarm clock is 30 seconds slower than the standard time: the alarm clock runs 59.5 minutes per hour, so it runs 60/59.5 minutes per minute.

So the alarm clock runs for 60 minutes, and the actual time is (60/59.5)×60 minutes.

Xiaoming's watch is 30 seconds faster than the alarm clock: the alarm clock runs for 60 minutes, the watch runs for 60.5 minutes, that is, (60/59.5)×60 minutes, and the watch runs for 60.5 minutes.

Then the watch goes 60.5/[(60/59.5)×60] minutes =(59.5×60.5)/(60×60) minutes per minute.

* * * 24×60 minutes a day, the watch goes [(59.5× 60.5)/(60× 60)] × 24× 60 =1439.9 minutes, minus1439.9-24× 60 =-0.

Method 2:

Let the watch actually go x seconds per hour.

Xiaoming's watch is 30 seconds faster than the alarm clock every hour, that is, the alarm clock runs 1 hour (3600 seconds), and the watch runs for 3630 seconds;

"The alarm clock is 30 seconds slower than the standard time every hour", that is, the standard time is 1 hour and the alarm clock runs for 3570 seconds.

Then in the standard time of 1 hour: 3630/3600 = x/3570, the solution is: x = 3599.75 (seconds).

Time difference between watch and standard time per hour: 3600-3599.75 = 0.25 (seconds)

Xiaoming's watch is 24× 0.25 = 6 seconds faster than the standard time day and night.