Two brothers, Jack and Jake, will both be running in the upcoming annual city marathon race. For this marathon, Jack believes that his time will be uniformly distributed between 229 and 304 minutes and Jake believes that his time will be uniformly distributed between 234 and 314 minutes. The brothers also believe that their times for this marathon will be independent of each other. Among all marathon races that the brothers have ran, Jack's personal best time is 260.2 minutes and Jake's personal best time is 255.9 minutes. For the upcoming annual city marathon race, find the probability that one brother runs faster than their personal best time.