Date-Range Slicer: Dynamically Change Data Aggregation on Chart based on selected date range

See if this measure helps. You need a data table for this to work.

This first measure just calculates the date range. You could incorporate that into Time Shown measure, but I kept it out for simplicity's sake.

Slicer Days = 
DATEDIFF(
    FIRSTDATE(ALLSELECTED('Date'[Date])),
    LASTDATE(ALLSELECTED('Date'[Date])),
    DAY
)

Then this does your actual calculation. I used "General Format" and put the measure in a card. You can get rid of that but you'll need some mechanism so your audience knows you switch from minutes to hours to days. I let anything above 90 also calculate to days to prevent a BLANK error showing up. You can change the math to show weeks or whatever you want.

Time Shown = 
SWITCH(
    TRUE(),
    [Slicer Days] <=3,
    FORMAT(SUM('Sample Data'[Minute Data]),"General Number") & " Minutes",
    [Slicer Days] > 3 && [Slicer Days] <=30,
    FORMAT(SUM('Sample Data'[Minute Data])/60,"General Number") & "Hours",
    [Slicer Days] > 30 && [Slicer Days] <= 90,
    FORMAT(SUM('Sample Data'[Minute Data])/(60*24), "General Number") & "Days",
    [Slicer Days] > 90,
    FORMAT(SUM('Sample Data'[Minute Data])/(60*24), "General Number") & "Days"
)

 My PBIX file if you want to play around with it.