You need to provide more detail.
1. What is the UX design? Imagine just creating the container without the content (the schedule). How long would it take to create just the container.
Think of it as building a house from scratch instead building a house with furnitures and interior designing applied. How long would it take just to build an empty house?
2. Now imagine you are adding the content. How are you presenting the content? Where are you getting the content. Think of designing the first section. How long does that take?
3. Now you got 40 sections. If let's say the first section takes 1 day, then a conservative bet is 40 sections will take 40 days.
4. Take a step back. What if I have 100 sections? Are there any recurring patterns? Maybe you can consolidate some logic and code that are common across sections. You can use this to reduce your estimates.
5. Don't forget the developer testing phase and the user acceptance testing phase. Maybe it's better to create the first section and show it to your client and ask them for early feedback if they like the user experience