# Thread: Application of rational function

1. ## Application of rational function

Consider the following context

Jamal owns a painting company that icludes two painters Bob and Anna. Jamal has modeled how long it takes each of them to paint a room where x = the number of square meters of the room. Bob takes ax-b minutes and Anna takes cx-d minutes, where "a" amd "c" are their painting speed and "b" and "d" are a amount of efficiency they have in painting a little faster than expected. Choose a reasonable a,b,c, and d and continue with the following.

Jamal wonders how to model Bob and Anna's combined time painting together.

Write the function for him and do the following with this function:
A) Give any asymptotes, zeros, and the y-intercept for this function,
B) Graph the funciton
C) How should the domain be restricted for this function?
D) Overlap Bob and Anna's individual time functions and discuss how they compare and contrast to the combined function.
E) What suggestion could you make for Jamal in his function models

Thank you very much for you help

2. ## Re: Application of rational function

$\dfrac{(ax-b)(cx-d)}{ax-b+cx-d} = \dfrac{acx^2-(bc+ad)x+bd}{(a+c)x-(b+d)}$