Answer:
Option B. t=5/3w ;1/3
Step-by-step explanation:
We are told that [tex]w[/tex] varies Inversely with [tex]t[/tex] thus generally speaking [tex]w[/tex]∝[tex]\frac{1}{t}[/tex] since they are inverted, otherwise if they were proportionally varied then [tex]w[/tex]∝[tex]t[/tex]. This means that there is a constant value ( [tex]a[/tex] ) for which [tex]w[/tex] is inversely proportional to [tex]t[/tex] and can be mathematically expressed as:
[tex]w=\frac{a}{t}[/tex] Eqn. (1)
Now since we are given the values of [tex]w=4[/tex] and [tex]t=\frac{5}{12}[/tex], we can plug them in Eqn. (1) and find our constant of proportionality [tex]a[/tex] as follow:
[tex]w=\frac{a}{t}\\ \\a=wt\\\\a=(4)(\frac{5}{12} )\\\\a=\frac{5}{3}[/tex]
Now that we have our constant we can find the new [tex]t[/tex] value for the second value of [tex]w=5[/tex] as follow:
[tex]w=\frac{a}{t} \\\\t=\frac{a}{w}\\ \\t=\frac{\frac{5}{3} }{5}\\\\t=\frac{5}{15}\\ \\t=\frac{1}{3}\\[/tex]
Therefore based on the options give, we can see that Option B. is correct since
[tex]t=\frac{5}{3w}[/tex] and for [tex]w=5[/tex], then [tex]t=\frac{1}{3}[/tex]