What conjunction (when or while) must I use in the sentence below?
The question is as follows. I’ve read several grammar books and they say that you can use a time clause with “when” or “while” and the past progressive to talk about an event that was in progress when a second event happened:
When Dave was eating, the doorbell rang.
When we were sitting in the library, the alarm went off.
While we were waiting for the train, it started to rain.
I cut my finger when I was peeling the potatoes.
So, “when” and “while” are interchangeable before the Past Progressive:
I met her when/while we were working for the same company.
After the grammar explanations there’s an exercise in which there’s a sentence where you have to put something.
_____ Dick was preparing lunch, he cut his finger badly.
I use “when” but – NO what I see in the key section of the book is only one word i.e. WHILE:
WHILE Dick was preparing lunch, he cut his finger badly.
The question is why can’t I use WHEN in this sentence if the rule permits?