2008 AMC 10B Problem 25

Number the pails so Michael is at pail $0$ and the truck at pail $1.$ Michael reaches pail $n$ at $40n$ seconds. The truck leaves pail $n$ at $50(n-1)$ seconds and arrives there at $50(n-1)-30$ seconds. Michael and the truck are together at pail $n$ when $50(n-1)-30\le 40n$ $\le 50(n-1),$ which simplifies to $5\le n\le 8.$ At pail $5$ they meet as the truck departs, at pails $6$ and $7$ Michael passes it, and at pail $8$ they meet as the truck arrives. Between pails $6$ and $7$ the truck must overtake Michael once more, so in total they meet $5$ times. Thus, the correct answer is B.