Kitaer is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complete the project in 2 hours. Kaitlyn can complete the project in 1 hours. Kitaer wants to know how long it will take them to complete the project together.

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Kitaer is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complete the project in 2 hours. Kaitlyn can complete the project in 1 hours. Kitaer wants to know how long it will take them to complete the project together.

Mathematics
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really confused on this?
x = time it takes for Cody to do the job alone y = time it takes for Kaitlyn to do the job alone z = time it take them to do the job together we're given x = 8 and y = 6. Solve for z \[\large \frac{1}{x}+\frac{1}{y}=\frac{1}{z}\] \[\large \frac{1}{8}+\frac{1}{6}=\frac{1}{z}\] \[\large \frac{3}{24}+\frac{4}{24}=\frac{1}{z}\] \[\large \frac{3+4}{24}=\frac{1}{z}\] I'll let you finish

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Other answers:

so 5/24?
no
? Please explain
\[\large \frac{3+4}{24}=\frac{1}{z}\] \[\large \frac{7}{24}=\frac{1}{z}\] cross multiply or take the reciprocal of both sides
Oh! Okay :) Sorry, I didn't notice that
so 7z=24
yes?
now fully isolate z
so 24/7
yep 24/7
is that the answer?
Can I ask another please?
sure, go ahead
Thanks :)
what are some key features that you can think of? any at all?
Maybe some degrees?
you mean the degree of the polynomial?
yes
what does the degree tell us?
how many answers it would have
I mean roots
close, the degree tells us the maximum number of roots, or x-intercepts, possible example: x^3 + 7x^2 + 9 has at most 3 roots. It could have 3 roots, or 2 roots, or just 1 root.
I understand. :)
the degree also tells us how many turning points there are number of turning points = (degree) - 1 example: degree = 3 means we have 2 turning points |dw:1437527865525:dw|
also, a degree 3 polynomial has 3 branches |dw:1437527902361:dw|
other key features: * y intercept * end behavior
the end behavior is explained in these articles http://www.purplemath.com/modules/polyends.htm http://www.mathwords.com/e/end_behavior.htm
Ok! Thank-you<3 So the answer would be
basically we need degress, y-intercepts, and end behaviors
knowing the degrees helps us determine how many roots max are possible it doesn't tell us the actual x-intercepts
you have to set the polynomial equal to 0 and solve for x
key features used to graph: x-intercepts y-intercept number of turning points (equal to degree - 1) end behavior also, a couple of other points doesn't hurt either
Hahha :) Thanks !
np

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