Final answer:
To find the equation of variation when m varies directly with p and inversely with t, we can use the formula for direct variation m=kp, where k is a constant of variation. Substituting the given values, we find the equation of variation to be m=6p. To incorporate the inverse variation with t, we divide both sides of the equation by t, resulting in m/t=6p.
Step-by-step explanation:
In this problem, we are given that m varies directly with p and inversely with t. This means that as p increases, m also increases, and as t increases, m decreases. We are also given that when m=6, p=1, and t=1/3. To find the equation of variation, we can use the formula for direct variation:
m = kp
where k is a constant of variation. To find the value of k, we can substitute the given values of m and p:
6 = k(1)
k = 6
So the equation of variation is m = 6p. Now, to incorporate the inverse variation with t, we divide both sides of the equation by t:
m/t = 6p/t
Simplifying further, we get m/t = 6p. This is the final equation of variation.