Borrowing from Dwain's sample data and Tally, here is my submission:

--== Dwain's setup ==--

declare @t as table (ptr int identity, START time, ENDD time)

insert into @t (START, ENDD)

SELECT '09:30', '10:30' union all

SELECT '10:00', '11:00' union all

SELECT '10:30', '11:30' union all

SELECT '09:30', '11:30' union all

SELECT '11:00', '11:30';

WITH Tally (n) AS

(

SELECT ROW_NUMBER() OVER (ORDER BY (SELECT NULL))

FROM (VALUES (0),(0),(0),(0),(0),(0)) a(a)

CROSS JOIN (VALUES (0),(0),(0),(0)) b(b)

)

--== And MM's solution ==--

select Tally.n as [Hour],SUM(calc.UpToENDD - calc.UpToSTART) as [TotalMinutes]

from Tally

left outer join @t as source

on Tally.n between datepart(hour,convert(datetime,source.START)) and datepart(hour,convert(datetime,source.ENDD))

outer apply (

select case when source.START is null then 0

when dateadd(hour,Tally.n,0)<convert(datetime,source.START) then datediff(minute,dateadd(hour,Tally.n,0),convert(datetime,source.START))

else 0

end as UpToSTART,

case when source.ENDD is null then 0

when Tally.n=datepart(hour,convert(datetime,source.ENDD)) then datediff(minute,dateadd(hour,Tally.n,0),convert(datetime,source.ENDD))

else 60

end as UpToENDD

) calc

group by Tally.n

order by Tally.n;