Ramanujan's Run

Ramanujan is running late to teach his lecture. He must run a mile across Cambridge to the lecture hall within ten minutes in order to get to his students on time. Beginning with attempt $n = 1$, he runs a distance of $x_n$ miles in $t_n$ minutes towards the lecture hall and repeats the process if he has (1) not yet arrived at the hall and (2) still has time to spare; the maximum value of $n$ is 3. The values of $x_n$ are chosen independently and uniformly at random between $0$ and $1$ miles, while the values of $t_n$ are chosen independently and uniformly at random between $0$ and $10$ minutes. If Ramanujan runs out of time during his $j$-th attempt, then time magically stops, allowing him to finish traveling the remainder of the $x_j$ miles. If Ramanujan runs equal to or more than a mile total within the ten minutes, then he arrives at the hall on time. What is the probability that Ramanujan gets to the lecture hall on time?