A rubber ball dropped on a hard surface takes a sequence of bounces, each one 2/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled at the time when it hits the surface for its fifth bounce?

A. 22 12/25 feet

B. 32 124/125

C. 25 124/125

D. 22 124/125

We create first the list of the distances that the ball will travel by multiplying the previous number by 2/5. That is,
10, 4, 8/5, 16/25, 32/125
(1) 10 + 4
(2) 4 + 8/5
(3) 8/5 + 16/25
(4) 16/25 + 32/125
(5) 32/125

Adding all the distances together will give an answer of 22.992 ft or equal to 22 124/125 ft. The answer is letter D.

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