How to write an inverse variation that relates to t and n + completing the table?

Question

The time t (in weeks) it takes workers to complete a project varies inversely with the number n of workers. It takes 3 workers 8 weeks to complete the project. Write an inverse variation equation that relates t and n. t=?

 

Complete the table:

n | 2 | 4 | 6 | 12 |

-------------------

t | ?  | ? | ? | ? |

 

 

Answer 1

This is one of the better questions posted. Far too many students ask us to analyze a graph we don't see, a table that isn't there, and so on. You did a nice job on yours, and get a (hopefully) helpful answer in return.

Inverse variation isn't complicated. While direct variations look like this:

Y = k * X

Inverse variation has this form:

Y = k / X

Your 3 workers in 8 weeks is a point in the form (3,8) and can be plugged in as:

8 = k / 3

Multiply both sides by 3 to solve:

24 = k

Now, you know the formula is:

Y = 24 / x.

The first value in your table is:

Y = 24 / 2 = 12

...and you can easily find the rest. Of course, I used the standard variables, but your question said (n,t), so adjust accordingly.