Running analysis on time data - estimating average time

General
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Would this work for you?
Note: In the future, please make you questions with a REPRoducible EXample (reprex) like this one

library(hms)
library(dplyr)

# Sample data
df <- data.frame(
    site = c(1, 2, 2, 3, 3, 3, 4),
    time.spent = c("05:00", "12:00", "06:43", "02:00", "17:00", "09:45", "06:00"),
    emissions = c(1.2, 3.6, 2.4, 9.6, 1.8, 5.3, 1.6))

df %>% 
    mutate(time.spent = as.numeric(parse_hm(time.spent))/3600)%>% 
    group_by(site) %>% 
    summarise(mean_time_spent = mean(time.spent),
              mean_emissions = mean(emissions))
#> # A tibble: 4 x 3
#>    site mean_time_spent mean_emissions
#>   <dbl>           <dbl>          <dbl>
#> 1     1            5              1.2 
#> 2     2            9.36           3   
#> 3     3            9.58           5.57
#> 4     4            6              1.6

Created on 2019-07-30 by the reprex package (v0.3.0)