Question

(Need some help gotta work a bunch of these, walk me through one I can do the rest)! Thanks!!
The time required to do a job, t, varies inversely as the number of people, p, who work on the job. Assime all people work on the job at the same rate. If it takes 13 people to paint the inside of an office building in 7 days, how long will it take 19 people to finish the same job?

Answer 1

13/7=19/x? thats my assumption,but that gave me the WRONG answer did i set it up wrong?

Answer 2

i think i might have done direct variation instead of inverse, not sure

Answer 3

yes

Answer 4

The inverse relationship can be written as follows:\[t:{1 \over p}\]

Therefore, \[13*7 = 19*t \rightarrow t = {13*7 \over 19}\]

Answer 5

could that have also been set up as\[f(p)=k/x\]

Answer 6

trying to clarify horrible textbook information sorry

Answer 7

the book actually says f(x)=k/x...i am just trying to relate t and p variables

Answer 8

What does k represent?

Answer 9

the variation constant/constant of proportionality

Answer 10

Okay. It would be \[f(p) = k/p\] In this case, \[k = t*p = 13*7 = 91\]

Answer 11

so really, for inverse it would be like 91/19 to show the variation constant proportional to 19 people?

Answer 12

Correct. An inverse relationship indicates that the two variables move in opposite directions. In this case, as the number of people increases, the time decreases. The proportionality constant tells us the magnitude by which these two variables move apart. To relate this to a simple linear equation of y = mx+b, m would be the proportionality constant. There is a direct relationship here. If we have y = m/x + b, we have an inverse relationship. As x increases, y decreases. For a given change in x, a larger m would indicate a smaller decrease in y.