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sprinter starts running

by sanju09 » Fri Jan 01, 2010 2:37 am
A sprinter starts running on a circular path of length 2 r meters. Her average Speed (in meters/minute) is r during the first 30 seconds, r /2 during next one minute, r/4 during next 2 minutes, r /8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?

(A) 4
(B) 8
(C) 12
(D) 16
(E) 32
Last edited by sanju09 on Sat Jan 02, 2010 2:59 am, edited 1 time in total.
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by Resurgent » Fri Jan 01, 2010 7:25 am
I am totally clueless ... not a good question to start the new year :?
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by linkinpark » Fri Jan 01, 2010 10:26 am
is it A?
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by sanju09 » Sat Jan 02, 2010 3:18 am
Resurgent wrote:I am totally clueless ... not a good question to start the new year :?
No Resurgent my dear... it's still a very happy new year

One complete round means a journey of 2 r meter here. Her motion is forming a geometric progression both speed-wise and time-wise:

Speeds (in meters/minute) r r/2 r/4 r/8 ...
Duration (in minutes) ½ 1 2 4 ...
Distances covered (in meters) r/2 r/2 r/2 r/2 ...

This means that after every 4th step in sequence, one round is complete (see r/2 + r/2 + r/2 + r/2 = 2 r); and the ratio of the time taken for the nth round to that for the previous round will be same as the ratio of the time taken for the 2nd round to that for the first round, generally speaking. Time taken in completing the first round can be had from the table above, as = ½ + 1 + 2 + 4 = 7.5 minutes, and that taken in completing the second round can be predicted to be = 8 + 16 + 32 + 64 = 120 minutes. Hence the required ratio will be [spoiler]120/7.5 = 16. D[/spoiler]

[spoiler]By the way, I had to make only one small change in the wording of the originally sent question to explain my point, can you tell what did I change there, Resurgent?[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



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by ace_gre » Sat Jan 02, 2010 1:44 pm
Hi,

In the original question you had mentioned radius of the circle as 2r..Now are you considering 2r as the circumference of the circle??
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