Question

Suppose that w and t vary inversely and that t = 1/5 one over five when w = 4. Write a function that models the inverse variation, and find t when w = 9.

Answer 1

if w and t vary inversely, then

w = k/t

we know that t = 1/5 when w = 4, so we can plug those values into the equation and find the value of k.

4 = k/(1/5)
4 = 5k
k =

now we use the value we just found for k, along with the value w = 9, and find the value of t. we'll have to rearrange the equation to solve for t:

w = k/t
wt = k
t = k/w

plug in the values and solve