MHB Write function to model combined rate

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The assignment involves modeling the combined rate of two pipes filling a swimming pool, where Pipe A takes 20 hours longer than Pipe B. The combined rate of both pipes filling the pool in 30 hours leads to the equation 1/x + 1/(x+20) = 1/30. The function R(x) that models this combined rate is given as f(x) = 1/x + 1/(x+20). To complete the assignment, the next step is to graph this function. Understanding the relationship between the rates of the two pipes is crucial for solving the problem.
calbeach900
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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.
 
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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)
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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