Question

If someone can dig a hole in 5 hours and someone else can in 6 hours if they do it together how many hours will it take

Answer 1

Think of it in terms of per unit of time, or the rate.

Person A can dig a hole in 5 hours, so he can do 1/5 of a hole per hour.
Person B can dig a hole in 6 hours, so he can do 1/6 of a hole per hour.

That means together they can dig a hole 1/5 + 1/6 = 11/30 of a hole per hour.

That means together they can dig a hole in 30/11 hours.

Or 2 and 8/11 of an hour.  Or roughly 2 hours and 44 minutes.