The first step to solve this problem is to convert the time taken to paint the room into a rate of work. This can be done by taking the reciprocal of the time.
When Samuel and Parker work together, they can paint the room in 6 hours. This means they paint at a rate of 1/6 of the room per hour.
Parker, working alone, can paint the room in 10 hours. This means his work rate is 1/10 of the room per hour.
We're interested in finding Samuel's work rate. Since the combined work rate (Samuel and Parker working together) is the sum of their individual work rates, we can find Samuel's work rate by subtracting Parker's work rate from the combined work rate.
Thus, we subtract Parker's rate (1/10) from the combined rate (1/6) to find Samuel's rate. This comes out to approximately 0.067 of the room per hour.
To find how long Samuel would take to paint the entire room alone, we again take the reciprocal of his work rate. This gives us approximately 15 hours.
So, if Samuel were to paint the room by himself, it would take him roughly 15 hours.