Excel SUMIF statement inside IF statement

I would like to create a SUMIF statement inside another statement. My data is below. I would like to create a SUM of time for 'Person A', but only if 'Type 2'. So for my formula is =SUMIF(B$1:B$5,"A",A$1:A5)

"Time . Person . Type

1:10 . A . 1

0:21 . B . 1

0:45 . A . 2

3:45 . C . 1

1:54 . A . 2"