هل أنت جاهزة للرحلة، أم أنت مشغولة في العمل؟

Because the sentence is addressing a woman. In Arabic, adjectives agree with the person they describe in gender and number. Since the subject is أنتِ (you, feminine singular), the predicates are feminine singular too:

• جاهزة = ready (to a woman)
• مشغولة = busy (to a woman)

If you were speaking to a man, you would say:

هل أنتَ جاهز للرحلة، أم أنتَ مشغول في العمل؟

In normal Arabic writing, أنت is often written the same for both masculine and feminine. The difference is usually clear from context or from agreement elsewhere in the sentence.

Here, the words جاهزة and مشغولة are feminine, so they show that أنت must mean you addressed to a woman.

If fully vowelled, the difference is visible:

• أنتَ = you (masculine singular)
• أنتِ = you (feminine singular)

هل is a question particle. It turns the sentence into a yes/no-type question or a question asking the listener to choose between alternatives.

So Arabic does not need a helping verb like do/are at the front the way English often does.
Instead of changing word order, Arabic can simply add هل.

Compare:

• أنت جاهزة للرحلة. = You are ready for the trip.
• هل أنت جاهزة للرحلة؟ = Are you ready for the trip?

أم is commonly used when the speaker is presenting two specific alternatives in a question and expects the listener to choose between them.

So here:

هل أنت جاهزة للرحلة، أم أنت مشغولة في العمل؟

means something like:

Is it A, or is it B?

By contrast, أو is the more general word for or. In many learner contexts, أو is translated as or, but in this kind of either/or question, أم is the more standard and elegant choice in Modern Standard Arabic.

It is repeated for clarity and balance:

هل أنت جاهزة للرحلة، أم أنت مشغولة في العمل؟

This gives a nice parallel structure:

• أنت جاهزة
• أنت مشغولة

In some contexts, Arabic can omit repeated words if the meaning is still clear, but repeating أنت here is very natural, especially in careful or formal Arabic.

In present-tense Arabic nominal sentences, the verb to be is usually not stated.

So:

• أنت جاهزة literally looks like you ready
• but it means you are ready

Likewise:

• أنت مشغولة = you are busy

This is one of the most important differences from English.

للرحلة is made of:

• لِـ = for / to
• الرحلة = the trip / the journey

Together:

• للرحلة = for the trip

With جاهز / جاهزة, Arabic often uses لِـ to express ready for:

• جاهز للامتحان = ready for the exam
• جاهزة للرحلة = ready for the trip

Yes, literally في العمل means in/at work. In natural English, we would usually say busy at work or busy with work.

With مشغول / مشغولة, Arabic can use a prepositional phrase like this to show what situation or area the person is occupied in.

A learner should also know that مشغولة بالعمل is very common too, and often feels closer to busy with work.

So these are related ideas:

• مشغولة في العمل = busy at work / occupied in work
• مشغولة بالعمل = busy with work

It is an adjective in form, but in this sentence it functions as the predicate of the sentence.

The structure is:

• أنت = subject
• جاهزة = predicate
• للرحلة = prepositional phrase attached to the predicate

So the sentence is not saying a ready woman in the sense of a noun phrase. It is saying you are ready.

The same applies to مشغولة in the second half.

It is a nominal sentence turned into a question.

Arabic has two broad sentence types:

• verbal sentence: usually starts with a verb
• nominal sentence: usually starts with a noun or pronoun

Here, the core statements are:

• أنت جاهزة للرحلة
• أنت مشغولة في العمل

Both are nominal sentences. Adding هل makes the whole thing into a question.

A fully vowelled version would be:

هَلْ أَنْتِ جَاهِزَةٌ لِلرِّحْلَةِ، أَمْ أَنْتِ مَشْغُولَةٌ فِي الْعَمَلِ؟

A few useful things to notice:

• أَنْتِ shows feminine you
• جَاهِزَةٌ and مَشْغُولَةٌ have feminine endings
• لِلرِّحْلَةِ is لِ + الرحلة
• final case endings like -ٌ and -ِ are often omitted in normal writing and pronunciation outside very formal contexts

Because of أم, the speaker is presenting two alternatives and usually expects the listener to choose one of them.

For example:

• أنا جاهزة للرحلة. = I am ready for the trip.
• أنا مشغولة في العمل. = I am busy at work.

So this is not just a general yes/no question. It is more like which of these two is true?

Not just the pronunciation. You would need to change the adjective forms too.

For a man, you would say:

هل أنتَ جاهز للرحلة، أم أنتَ مشغول في العمل؟

Changes:

• جاهزة → جاهز
• مشغولة → مشغول
• and if fully vowelled, أنتِ → أنتَ

So gender agreement matters in multiple places.