I need the solution for this question in detailed steps especially for the question in b)

2.47 A man begins a car trip to visit his in-laws. The total distance is 60 miles, and he starts off at a speed of 60 miles per hour. After driving exactly 1 mile, he loses some of his enthusiasm for the journey, and (instantaneously) slows 52 Chap. 2 Mathematical Preliminaries down to 59 miles per hour. After traveling another mile, he again slows to 58 miles per hour. This continues, progressively slowing by 1 mile per hour for each mile traveled until the trip is complete. (a) How long does it take the man to reach his in-laws? (b) How long would the trip take in the continuous case where the speed smoothly diminishes with the distance yet to travel