# Thread: Rational Functions Application Question

1. ## Rational Functions Application Question

Hey Guyzz,
Can you help me with this Application Problem; its all about ration functions.

Patricia and Chelsea can build a bike together in an hour and a half. However, if Patricia worked with Tanesha they can build the same bike 10 minutes faster. Working by herself, Patricia can build a bike 2 hours faster than Tanesha.
a) How long will it take for each of the girls to build a bike by herself.
b) How long will it take for the three of them to build a bike together.

Thank you.

2. Originally Posted by MordernWar2
Hey Guyzz,
Can you help me with this Application Problem; its all about ration functions.

Patricia and Chelsea can build a bike together in an hour and a half. However, if Patricia worked with Tanesha they can build the same bike 10 minutes faster. Working by herself, Patricia can build a bike 2 hours faster than Tanesha.
a) How long will it take for each of the girls to build a bike by herself.
b) How long will it take for the three of them to build a bike together.

Thank you.
You should first consider the following simpler problem and use it as a stepping stone:

If it takes Ernie 3 hours to make a bike and Bert 4 hours to make a bike, how long does it take them to make a bike together?

3. Originally Posted by MordernWar2
Hey Guyzz,
Can you help me with this Application Problem; its all about ration functions.

Patricia and Chelsea can build a bike together in an hour and a half.
However, if Patricia worked with Tanesha they can build the same bike 10 minutes faster. Working by herself, Patricia can build a bike 2 hours faster than Tanesha.
a) How long will it take for each of the girls to build a bike by herself.
b) How long will it take for the three of them to build a bike together.
let p = number of hours for patricia to complete a job.
rate she works is (1 job)/(p hrs)

c = number of hours for chelsea to complete a job
(1 job)/(c hrs)

t = number of hours for tanesha to complete a job
(1 job)/(t hrs)

Patricia and Chelsea can build a bike together in an hour and a half.

$\displaystyle \left(\frac{1}{p} + \frac{1}{c}\right) \cdot \frac{3}{2} = 1$ job done

if Patricia worked with Tanesha they can build the same bike 10 minutes faster.

$\displaystyle \left(\frac{1}{p} + \frac{1}{t}\right) \cdot \left(\frac{3}{2}-\frac{1}{6}\right) = 1$ job done

Working by herself, Patricia can build a bike 2 hours faster than Tanesha.

$\displaystyle \frac{1}{p} = \frac{1}{t-2}$

solve the system of equations for the three rates.

4. Hey Skeeter,

I have one question when you said solve this equations for three rates, can you please explain what do you mean and can you please give me and example.

Thank you.

5. Originally Posted by MordernWar2
Hey Skeeter,

I have one question when you said solve this equations for three rates, can you please explain what do you mean and can you please give me and example.

Thank you.
He means solve the equations he gave you for p, c and t. That's your job. I suggest you start by substituting the third equation into the second equation and solving for t.

If you need more help, please show what you've done and say where you get stuck.
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}