Sum the time durations
Javascript ES6, 138 chars

Function, 139

Takes string as an argument and writes output to console:

f=s=&gt;(r=0,s.replace(/(\d\d?):(\d\d)(:(\d\d))?/g,(m,a,b,x,c)=&gt;r+=x?+c+b*60+a*3600:+b+a*60),console.log("%dh %dm %ds",r/3600,r%3600/60,r%60))


Program, 138

prompt(r=0).replace(/(\d\d?):(\d\d)(:(\d\d))?/g,(m,a,b,x,c)=&gt;r+=x?+c+b*60+a*3600:+b+a*60),console.log("%dh %dm %ds",r/3600,r%3600/60,r%60)


Test for function

f("View the Welcome video.\n\
Video: 10:37 min.\n\
View the video introduction to the course.\n\
Video: 3:30 min. View the video of how to use the Lesson Overview.\n\
Video: 9:13 min.\n\
View the video overview of how to use the Epsilen system to share your work.\n\
Video: 03:15 min.\n\
View the video to learn about the State of Texas Assessment of Academic Readiness (STAAR).\n\
Video: 1:05:26 min.")


Output

"1h 32m 1s"