This problem came from my physics book, but the pre-calculus forum seems the most appropriate, as there is no physics forum, unless I missed it. I was able to solve the problem, but in a way that was not true to the description, and am wondering what the algebraic solution is. This is the problem description:
The way I solved this was by using two functions, one with a slope of 77.8 km/hr, with x and y intercept at the origin, and the other with a slope of 89.5 km/hr with an x-intercept of (.367 hr, 0 km), and a y-intercept of (0 hr, -32.8 Km), this y intercept computed by figuring how much displacement occurs in 22 minutes at 89.5 Km/hr. So my two equations were y = 77.8x and y = 89.5x - 32.8. Plotting them on a TI-89 and noting the intersection (2.8 hr, 218 Km), I arrived at the correct answer.A person takes a trip, driving with a constant speed of 89.5 km/hr except for a 22.0-min rest stop. If the person's average speed is 77.8 km/hr, how much time is spent on the trip and how far does the person travel?
However, how to figure this out algebraicly is stumping me, and the book does not have a worked-out example like this problem. This is very frustrating, as I feel that I'm missing something very basic here.