You could separate by spaces, but I think it's easier to just read it in with a space as the separator to begin with:
bpd <- readr::read_delim("name age start week1 week2 week3
Anne 35 2014-03-27 100/80 100/75 120/90
Ben 41 2014-03-09 110/65 100/65 135/70
Carl 33 2014-04-02 125/80 <NA> <NA>", delim = " ", na = "<NA>")
bpd
#> # A tibble: 3 x 6
#> name age start week1 week2 week3
#> <chr> <dbl> <date> <chr> <chr> <chr>
#> 1 Anne 35 2014-03-27 100/80 100/75 120/90
#> 2 Ben 41 2014-03-09 110/65 100/65 135/70
#> 3 Carl 33 2014-04-02 125/80 <NA> <NA>
Created on 2020-04-27 by the reprex package (v0.3.0.9001)