t = 36
Step-by-step explanation:
given that m varies directly with t then the equation relating them is
m = kt ← k is the constant of variation
to find k use the condition m = 4 when t = 12 , then
4 = 12k ( divide both sides by 12 )
[tex]\frac{4}{12}[/tex] = k , that is
k = [tex]\frac{1}{3}[/tex]
m = [tex]\frac{1}{3}[/tex] t ← equation of variation
when m = 12 , then
12 = [tex]\frac{1}{3}[/tex] t ( multiply both sides by 3 to clear the fraction )
36 = t