We can solve this problem by determining how far the ball travels on each bounce. Once it has hit the ground the 4th time, it will have gone:
Down, up, down, up, down, up, down.
Now, we calculate how far each of these distances are.
Since the first drop is 10 feet, the ball will go up to 5 feet. Then it will fall 5 feet and go up 2.5 feet. The ball will then fall 2.5 feet, and rise 1.25 feet and fall 1.25 feet. Now, we add all these numbers up.
10 + 5 + 5 + 2.5 + 2.5 + 1.25 + 1.25 = 27.5, so the ball will have travelled 27.5 feet.
