can someone explain the solution to me?

Question

if working alon, Phil can complete a job in R hours and henry can complete the same job in S hours, how many hours would it take them to complete the job TOGETHER?
solution:
H/R + H/S= 1 okay, so why the equals to 1? why 1?
answer: H= RS/S+R

Answer 1

In one hour, Phil can do 1/R of the job and Henry can do 1/S of the job. So together they can do
1/R + 1/S
= S/RS + R/RS
= (S+R) / RS
of the job in one hour.
In H hours they can do H(S+R) / RS of the job. When this is 1, it means they have done all of the job. So we want
H (S+R) / RS = 1
and therefore H = RS / (S+R).

The 1 comes in because that is the proportion of the job that we want to be completed - i.e. all of it.

Answer 2

1 stands for the completed job.. u have to equate it to the terms to find out how much hours it needs to be completed, provided that Phil and Henry worked for the same time.

H = hours
1/R = rate of work of Phil
1/S = rate of work of Henry
H/R = rate of work of Phil multiplied by working time
H/S = rate of work of Henry multiplied by working time

therefore, with the term H/R + H/S= 1, you are saying that it took Phil and Henry H hours working together to complete the job (1). by isolating H, you get to find out how many hours they worked

Answer 3

you rearranged the equation wrong H = R+S

as R/H + S/H = 1