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

Answer:

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

Step-by-step explanation:

We are told that $w$ varies Inversely with $t$ thus generally speaking $w$∝$\frac{1}{t}$  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:

$w=\frac{a}{t}$        Eqn. (1)

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

$w=\frac{a}{t}\\ \\a=wt\\\\a=(4)(\frac{5}{12} )\\\\a=\frac{5}{3}$

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

$w=\frac{a}{t} \\\\t=\frac{a}{w}\\ \\t=\frac{\frac{5}{3} }{5}\\\\t=\frac{5}{15}\\ \\t=\frac{1}{3}$

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

$t=\frac{5}{3w}$ and for $w=5$, then $t=\frac{1}{3}$