Teaser 2894: Time duality

From The Sunday Times, 11th March 2018 [link]

After a good breakfast, Seb decided on 40 winks. He noted the time on his digital clock as he dozed off. When he woke up a little later that day, not fully alert, he saw the display reflected in a mirror and was amazed by how long he seemed to have slept. This was in fact 10 times the length of his nap. Next day, a similar thing happened: he fell asleep at the same time and slept a little less, but when he woke, the mirror led him to believe he had slept for 20 times as long as he had. (All times were whole numbers of minutes after midnight).

At what time did he fall asleep?

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