Roland and Sam wash dogs to make extra money. Roland can wash all of the dogs in 4 hours. Sam can wash all of the dogs in 3 hours. How long will it take them to wash the dogs if they work together?

To complete the 100% of (the job) washing, Roland needed 4 Hours & Sam, 3 hour,

Mind you 100% = 1

Find for each one the (job) achieved in 1 hour:

Roland achieved 1/4 & Sam 1/3 each one in 1 hour.

In one hours both will achieve 1/4+1/3 = 7/12

So they will complete 7/12 (of the job) in 1 hour & for a time = t they will complete 100% (or 1) of the job, that is 1/t = 7/12 & t=12/7 = 1.71 hour