Is there any difference between 頼む and 聞く? I've checked a few dictionaries,
and it seems to me that maybe 頼む is more humble and 聞く more generic. Would
that be it? Are they generally interchangeable?

I think they both mean 'ask'. For example:

友だちに何時と聞きました。 友だちに何時と 頼み ました。
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meaning
Difference between 頼む and 聞く
[聞]{き}く refers to a **request for information**. Note that this particular
usage of the word is often written as 訊く as well. Examples:

  * [友]{とも}だちに[何時]{なんじ}と[聞]{き}きました。 (Asked a friend what time it was.)
  * [自分]{じぶん}の[胸]{むね}に[聞]{き}け ("Ask your heart." / "Look inside yourself.")

[頼]{たの}む is all about a **request for action**. Examples:

  * [代筆]{だいひつ}を頼む (Ask someone to write a letter. / "Please write a letter [for me].")
  * [口外]{こうがい}しないよう頼む ("Don't reveal this [secret].")

As you can see with these definitions, 「友だちに何時と頼みました」 doesn't really make any
sense. I don't know of any examples I've seen where the two words can be
switched out while still retaining the same meaning. This is a good example of
the fact that even though two words may _translate_ similarly, that doesn't
necessarily mean that they function similarly in the original language. :)

(other example sentences from goo[辞書]{じしょ}:
[聞く](http://dictionary.goo.ne.jp/leaf/jn2/51102/m0u/%E8%A8%8A%E3%81%8F/),
[頼む](http://dictionary.goo.ne.jp/leaf/jn2/138138/m0u/))
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聞く means 'ask (a question)'.

> 友達に何時か聞きました。I asked a friend what time it was.

頼む means 'ask someone to do something'.

> 友達に助けてくれと頼みました。 I asked a friend to help me.
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「[頼]{たの}む」 means "to ask a favor", "to make a request", etc.

「[聞]{き}く」 means "to ask (a question)"

I cannot think of a situation where 「[頼]{たの}む」 and 「[聞]{き}く」 are
interchangeable except for in a **_very_** informal conversation where a
question being asked involves a request. Careful speakers, however, would try
to avoid this.

「[車]{くるま}を[貸]{か}してくれる **か** (or **かどうか** )、スミスに **聞いて** みよう。」= "Let's ask
Smith if he could lend us his car!"

To say the same thing using 「頼む」, one will need to make a change in the middle
part as well.

「車を貸してくれる **よう** (or **ように** )、スミスに **頼んで** みよう。」

Careful speakers would not swap 「頼む」 for 「聞く」 or vice versa in the example
sentences above. That, of course, means that some people actually would do
that.

Let's take a look at your sentences.

「友だちに何時と聞きました。」＝「友達に『何時？』と **聞きました** 。」 = "I asked my friend what time it
was."

This is a good sentence and you could NOT use 「頼む」 here.

「友だちに何時と **頼みました** 。」

This makes no sense, I am afraid. Where is the request that is being made?

To use 「頼む」 correctly, one could alter the sentence to:

「友達に5時に来るように頼みました。」 or

「友達に5時に来てと頼みました。」

Naturally, you could NOT use 「聞く」 in these sentences.

= "I asked my friend to come at 5 o'clock."
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