Suppose that w and t vary inversely and that t = when w = 4. Write a function that models the inverse variation, and find t when w = 9. (1 point)

t = 1/5w; 4/45
t = 1/5w; 1/5
t = 1/20w; 1/80
t = 4/5w; 4/45

Question

Suppose that w and t vary inversely and that t =  when w = 4. Write a function that models the inverse variation, and find t when w = 9.  (1 point)

t = 1/5w; 4/45
t = 1/5w; 1/5
t = 1/20w; 1/80
t = 4/5w; 4/45

whpalmer4 · Answer

t = ??? when when w = 4?

whpalmer4 · Answer

Keep the extra "when" as a souvenir :-)

anonymous · Answer

@whpalmer4 t = 1/5

anonymous · Answer

@whpalmer4

whpalmer4 · Answer

We have inverse variation here, so wt = k where k is a constant.  If w doubles, t is halved.  We also know that t = 1/5 and w = 4.  We can solve for k by simply doing $$k = (\frac{1}{5}*4) = \frac{4}{5}$$ so our equation is $$wt = \frac{4}{5}$$ or $$w=\frac{4}{5t}$$ or $$t=\frac{4}{5w}$$

For the second part, just plug in w = 9 in our final formula to get the value of t.

whpalmer4 · Answer

As a quick check, we roughly doubled w, so t should be roughly half of what it was.  half of 1/5 is 1/10, and 4/45 is about 1/11, so our answer seems plausible.