How Would You Handle This Situation?

Here is the basic situation.

(1) I have 2 packages that run independently of eachother.
(2) Both are scheduled in SQLServer Agent Jobs as separate jobs.
(3) Job A is scheduled to run every 12 hours and Job B is scheduled to run every 10 minutes.
(4) However, I want to prevent Job B from running if Job A happens to be running.
(5) It is unknown exactly how long Job A will take to finish so I can't schedule Job B around it.

The way I wanted to approach this situation is as follows.

Within Job A's package, create a "marker" file when the package starts and delete it when the package finishes. So the existence of this marker file will tell Job B's package if it should run or not.

The concept is simple, but I'm not sure how to implement this.

For example, to create the marker file, I would use a File System Task, but I don't see an option in there to "create file". (However, I do see an option for "delete file".) Also, what task would I use in Job B's package to check if the marker file exists.

Lastly, If you have better approach, I would like to hear about it.

Thank you.