Question

When p = 12, t = 2, and s=1/6r = 18. If r varies directly with p and inversely with the product of s and t, what is the constant of variation?

Answer 1

R$\alpha \frac{p}{st}$
r=k$\frac{p}{st}$
18=12$\frac{k}{1/6*2}$
18=12*3k
k=$\frac{1}{2}$

Answer 2

R α p/(st)

r =  kp/(st)

Where k = constant of proportionality

r = 18, p = 12, t = 2 , s = 1/6

r =  kp/(st)

18 =  k*12/((1/6)*2)

18 = 12k /(1/3)

18 = 12*3*k

18 = 36k

18/36 = k

1/2 = k

k = 1/2

Constant of variation = 1/2 = 0.5