[WIP] Add backend tasks list for subway travel time calculation

[Claude]

Thanks for assigning this issue to me. I'm starting to work on it and will keep this PR's description up to date as I form a plan and make progress.

Original prompt

---

This section details on the original issue you should resolve

<issue_title>아이디어 스텝 남겨줘</issue_title>
<issue_description>지하철 출발역 부터 도착역 까지 걸리는 시간을 계산하는 웹을 만들건데

백엔드에서 필요한 작업 리스트업해줘</issue_description>

Comments on the Issue (you are @claude[agent] in this section)

• Fixes 아이디어 스텝 남겨줘 #5