Question

Suppose that w and t vary inversely and that t=1/5 when w=4. write a function that models the inverse variation and find t when w=9
A. t= 1/5w; 4/45
B. t= 1/5w; 1/5
C. t= 1/20w; 1/80
D. t= 4/5w;4/45

Answer 1

Two variables vary inversely if their product is constant (does not change). The variables w and t vary inversely so their product wt = k were k is a constant. Solving this for t we get t=k/w

We are told that w = 4 and t = 1/5 so we know their product wt = (4)(1/5) = 4/5. This is what I called k before.

Therefore the relationship between w and t can be modeled by t = (4/5) / w. That is, t = 4 / 5w

Further, when w = 9, we find t by substituting 9 for w in the equation just found and obtain: t = 4 / [(5)(9)] = 4/45. That is, when w = 9, t = 4/45.

This mean choice D is the correct answer.