Question

Suppose that w and t vary inversely and that t = 5/12

when w= 4. Write a function that models the inverse
variation and find t when w = 5.
A. T=5/12w; 5/12
B.t=5/3w;1/3
C.t=5/48w;5/192
D.t=5/12w;1/3

Answer 1

Option B. t=5/3w ;1/3

Explanation:

We are told that
`w` varies Inversely with
`t` thus generally speaking
`w`∝
`(1)/(t)` since they are inverted, otherwise if they were proportionally varied then
`w`∝
`t`. This means that there is a constant value (
`a` ) for which
`w` is inversely proportional to
`t` and can be mathematically expressed as:

`w=(a)/(t)` Eqn. (1)

Now since we are given the values of
`w=4` and
`t=(5)/(12)`, we can plug them in Eqn. (1) and find our constant of proportionality
`a` as follow:

`w=(a)/(t)\\ \\a=wt\\\\a=(4)((5)/(12) )\\\\a=(5)/(3)`

Now that we have our constant we can find the new
`t` value for the second value of
`w=5` as follow:

`w=(a)/(t) \\\\t=(a)/(w)\\ \\t=((5)/(3) )/(5)\\\\t=(5)/(15)\\ \\t=(1)/(3)\\`

Therefore based on the options give, we can see that Option B. is correct since

`t=(5)/(3w)` and for
`w=5`, then
`t=(1)/(3)`