# Write function to model combined rate

#### calbeach900

##### New member
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.

The assignment question I am stuck on is 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. After I have come up with the R(x) function, I will need to graph that function for my assignment.

I already know how to solve for the individual times for each pipe where:
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 me the rates of the individual pipes.

The assignment question I am stuck on is I can't figure out how to write the 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.

#### Country Boy

##### Well-known member
MHB Math Helper
You have already done that! In what you have written you have taken x to BE the time it takes for pipe B to to fill the tank by itself so writing "in relation to the time it takes for pipe B to do it by itself" means just writing a function in terms of x. And you said that the combined rates is1/x+ 1/(x+ 20). Your function is f(x)=1/x+ 1/(x+20)

• topsquark