How to write a function R(x) to be graphed

Question

The assignment question I am stuck with is how do I write a function R(x) that models the combined rate of the two pipes in relation to the time it takes for pipe B to do it by itself? After I have come up with the R(x) function, I will need to graph that function for my assignment.

The assignment states:

Pipe A takes 20 hours longer to fill swimming pool than pipe B. Together, pipe A and pipe B can fill the swimming pool in 30 hours.

I already learned how to solve for the individual times for each pipe where the formula to use is:

1/job 1 + 1/job 2 = 1/total

time to fill with Pipe B = x

time to fill Pipe A = x+20

1/x + 1/(x+20) = 1/30

Solving for x will give the rates of the individual pipes.

The problem i have currently is I don't know how to write a function R(x) that models the combined rate of the two pipes in relation to the time it takes for pipe B to do it by itself in order to graph it.

Would the function R(x) modeling that combined rate of the two pipes be R(x) = 1/x + 1/(x+20) ? I tried to graph R(x) = 1/x + 1/(x+20) and it doesn't seem right. So I doubted that I had the correct R(x) function.

Answer 1

R(x) represent the total.

So start with

1/R(x) = 1/x + 1/(x+20)

Then solve for R(x).