The pronunciation of "ate"

Solution 1:

That's just a regional pronunciation. It's non-standard but not completely uncommon. If I had to guess, I'd say rural midwestern America, where a lot of the different vowel sounds all get pronounced the same --although Peter Shor's comment above seems to imply it might also be a Cockney accent. (I'm not all that familiar with British accents, so I don't know which might fit best.)

Solution 2:

The traditional RP pronunciation of ate is /ɛt/. The second edition of the Oxford English Dictionary agrees:

/ɛt/, occasionally /eɪt/.

I believe Charivarius also has /ɛt/. From his famous poem about the inconsistent spelling of English, The Chaos:

Reefer does not rhyme with deafer,
Feoffer does, and zephyr, heifer.
Dull, bull, Geoffrey, George, ate, late,
Hint, pint, senate, but sedate.

However, it is my impression that /eɪt/ has become more and more common everywhere, even in RP.