Add multiple linux timing results (output in seconds)

If there are multiple files with timing results resulting from Linux 'time' command:
$ cat outputFile* | grep real
real 4m5.047s
real 2m51.264s
real 2m52.414s
real 2m52.293s

And these timings need to be converted into seconds and added into a single number (e.g., 761.018), use the following command:
cat outputFile* | grep real | cut -f 2 | sed 's/m/*60+/' | sed 's/s//g' | bc | awk '{ printf "%s", $0 "+" }' | sed '$s/.$/\n/' | bc