2022 SSMO Accuracy Round Problems/Problem 7

Problem

After a robber drives in a car for (not necessarily integral) minutes, the car goes at miles per hour. Whenever the car's speed drops below miles per hour, the robber switches into a new car with no time loss. A police car can drive at a constant speed of 117 miles per hour. Given that the robber starts 1 hour before the police car, how many minutes will pass between when the police car starts and when the police car catches up to the robber?