A rubber ball is dropped from a height of 100 feet.  Each the time ball bounces, it rises to a height $\frac{2}{5}$ of the previous height.  Find the total distance the ball travels, in feet.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A rubber ball is dropped from a height of 100 feet.  Each the time ball bounces, it rises to a height $\frac{2}{5}$ of the previous height.  Find the total distance the ball travels, in feet.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{700}{3}
A rubber ball is dropped from a height of 100 feet.  Each the time ball bounces, it rises to a height $\frac{2}{5}$ of the previous height.  Find the total distance the ball travels, in feet.
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