itizikan no entyou wo tanomou.

いちじかん の えんちょう を たのもう。

• 一時間 = いちじかん
• 延長 = えんちょう
• 頼もう = たのもう

So the full reading is:

いちじかん の えんちょう を たのもう。

一時間の延長 means a one-hour extension or an extension of one hour.

Here:

• 一時間 = one hour
• 延長 = extension
• の links the two nouns

So の is working like a noun-connector. It shows that the extension is specifically for one hour.

You can think of it as:

• 延長 = extension
• 一時間の延長 = a one-hour extension

を marks 延長 as the thing being requested.

The verb 頼む means to ask for, to request, or to ask someone to do something.
In this sentence, what is being requested is 一時間の延長.

So:

• 一時間の延長 = the one-hour extension
• を = marks it as the object
• 頼もう = let’s ask for it / I’ll ask for it

頼もう is the volitional form of 頼む.

• dictionary form: 頼む
• volitional form: 頼もう

The volitional form often means:

• let’s request
• I’ll request
• why don’t we request

Which one it means depends on context.

So 一時間の延長を頼もう。 could sound like:

• Let’s ask for a one-hour extension.
• I’ll ask for a one-hour extension.

In casual speech, this kind of sentence often sounds like a suggestion or a decision.

Because the speaker is not personally doing the extending; they are asking for an extension.

Compare:

• 延長する = to extend
• 延長を頼む = to ask for an extension

So:

• 一時間の延長を頼もう = let’s ask for a one-hour extension
• 一時間延長しよう = let’s extend it by one hour

The nuance is different.
頼む focuses on making a request, probably to staff, a clerk, a receptionist, and so on.

The person being asked is simply omitted because Japanese often leaves out information that is obvious from context.

For example, this might mean:

• asking the staff
• asking the receptionist
• asking the karaoke desk
• asking the hotel front desk

A fuller sentence could be something like:

店員に一時間の延長を頼もう。
= Let’s ask the staff for a one-hour extension.

Here, に would mark the person being asked. But if everyone already knows who that is, Japanese often drops it.

Yes, it is plain/casual.

The main clues are:

• 頼もう is plain style
• there is no です / ます
• the sentence ends in a direct, informal way

This sounds natural in casual conversation, inner thoughts, or speaking to someone close.

If you wanted to say it more politely, you might say something like:

一時間の延長をお願いしましょう。
or
一時間延長をお願いしましょう。

It can be either.

The Japanese volitional form often covers both:

• let’s do X
• I’ll do X

So the exact feeling depends on context:

• If speaking to another person: Let’s ask
• If thinking to oneself: I’ll ask

Japanese often leaves that ambiguity in place if the situation makes it clear enough.

Sometimes you may see 一時間延長 as a compact expression, especially in signs, ads, menus, or service-related wording.

For example:

• 一時間延長無料 = one-hour extension free

But in a full sentence like this, 一時間の延長 sounds very natural and standard.

So:

• 一時間の延長を頼もう = very normal as a sentence
• 一時間延長を頼もう = possible in some contexts, but less neutral/basic for learners

Yes, very likely.

The sentence does not say what is being extended, because that is probably already understood from the situation.

Depending on context, it could be:

• a reservation
• a karaoke room
• a hotel stay
• a rental
• a deadline
• a meeting

Japanese often omits this kind of information when it is obvious from context.
So the sentence focuses only on the action that matters right now: asking for one more hour.