SOLUTION: If a friend and I were climbing up the side of a building and it takes us ten seconds to reach the top. What fraction of the building would we have covered in 8 seconds if for ever

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Question 47063: If a friend and I were climbing up the side of a building and it takes us ten seconds to reach the top. What fraction of the building would we have covered in 8 seconds if for every second the distance doubled?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Say that in the 1st second, the distance covered is a.
It takes 10 seconds to reach the top.
For every second the distance doubles
sec distance
(1) a
(2) 2a
(3) 4a
(4) 8a
(5) 16a
(6) 32a
(7) 64a
(8) 128a
(9) 256a
(10) 512a
so, at the end of 8 sec the total distance covered is
a + 2a + 4a + 8a + 16a + 32a + 64a + 128a = 255a
At the end of 10 sec the top is reached and the distance covered is
a + 2a + 4a + 8a + 16a + 32a + 64a + 128a + 256a + 512a = 1023a
The fraction of the building height covered in 8 sec is
255a / 1023a = .2493