The potholes in a road occur as a Poisson process of rate 4 per mile. So, $R(t) =$ "the number of potholes in the first $t$ miles of the road". The situatuion we are given is that "A repair crew travel along the road, repairing each pothole they pass until they have repaired 10 potholes. What is the expectation of the distance they travel?".
In my mind, we know that for every mile we travel, we expect to see $4$ potholes. Then after $2.5$ miles, on average, we would have seen $10$ potholes. So is it that simple? Would we expect the crew to have just travelled $2.5$ miles?
EDIT to formalise my argument: Let $S_i$ denote the $i$th interarrival time. Then $S_i \sim \exp(4)$ by definition. We want to solve $\mathbb{E}(S_1 +S_2 + \dots +S_{10}) = \mathbb{E}(S_1)+\mathbb{E}(S_2)+\dots +\mathbb{E}(S_{10})$ which is equal to $(10/4) = 2.5$.