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 November 14th, 2017, 06:39 AM #1 Newbie   Joined: Nov 2017 Posts: 1 Thanks: 0 Please answer the following question. Consider the following context Jamal owns a painting company that includes 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" and "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 function 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 Last edited by skipjack; February 20th, 2018 at 11:07 PM.
 February 20th, 2018, 11:07 PM #2 Global Moderator   Joined: Dec 2006 Posts: 19,704 Thanks: 1804 Sorry about delay.
February 21st, 2018, 07:33 AM   #3
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Quote:
 Originally Posted by luckjoehkg Please answer the following question. Consider the following context Jamal owns a painting company that includes 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" and "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,
When two people work together, their rates add. Bob works at the rate of $\frac{1}{ax- b}$ "room per minute" and Anna works at the rate of $\frac{1}{cx- d}$ so, together, they work at the rate of $\frac{1}{ax- b}+ \frac{1}{cx- d}= \frac{cx- d+ ax- b}{(ax- b)(cx- d)}= \frac{(a+c)x- (b+ d)}{(ax-b)(cx-d)}$.

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 B) Graph the function
There is a simple graphing program at
https://www.desmos.com/calculator

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 C) How should the domain be restricted for this function?

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 D) Overlap Bob and Anna's individual time functions and discuss how they compare and contrast to the combined function.
"Overlap"? Perhaps that means draw the graphs of the two functions on the same graph on which you did (B).

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 E) What suggestion could you make for Jamal in his function models? Thank you very much

Last edited by Country Boy; February 21st, 2018 at 08:32 AM.

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