Write function to model combined rate

In summary, the assignment requires the creation of a function R(x) that models the combined rate of two pipes in relation to the time it takes for pipe B to fill the swimming pool by itself. The individual times for each pipe can be solved using the equation 1/x + 1/(x+20) = 1/30, where x represents the time for pipe B. The function R(x) is equivalent to f(x) = 1/x + 1/(x+20).
  • #1
calbeach900
1
0
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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  • #2
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)
 

What is a combined rate function?

A combined rate function is a mathematical function that models the combined rate of two or more processes or events. It takes into account the individual rates of each process and calculates the overall rate at which the processes occur together.

Why is it important to write a function to model combined rate?

Writing a function to model combined rate is important because it allows us to better understand and analyze complex systems or processes that involve multiple rates. It also enables us to make predictions and optimize the overall rate by adjusting the individual rates of each process.

What are the key components of a combined rate function?

The key components of a combined rate function include the individual rates of each process, the weights or proportions of each process, and any other variables or factors that may affect the overall rate. These components are used to calculate the combined rate using a mathematical formula.

How can a combined rate function be applied in real-life situations?

A combined rate function can be applied in various real-life situations, such as in finance to calculate interest rates, in chemistry to model reaction rates, and in biology to study population growth. It can also be used in business and economics to analyze production rates and in sports to predict team performance based on individual player statistics.

What are some common mathematical models used to write a combined rate function?

Some common mathematical models used to write a combined rate function include linear functions, exponential functions, and logarithmic functions. These models can be used to represent different types of relationships between the individual rates and the overall rate, depending on the specific situation or system being studied.

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