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sprinter starts running

by sanju09 » Fri May 07, 2010 2:38 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


I have edited it just once after the first two posts. Can any of iamseer and ansumania tell what I changed there?
Last edited by sanju09 on Sat May 08, 2010 3:31 am, edited 1 time in total.
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by iamseer » Fri May 07, 2010 9:59 am
IMO D
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by ansumania » Sat May 08, 2010 3:18 am
pl. explain........
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by clock60 » Sat May 08, 2010 4:15 am
sanju09 wrote: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


I have edited it just once after the first two posts. Can any of iamseer and ansumania tell what I changed there?
i also got 16 but solution is rather tiresome
i think the main concept here is GP
time taken on the the first lap
1/2+1/2*2+1/2*2^2+1/2*2^3, as
r*1/2+r/2*1+r/4*2+r/8*4=2r -first lap

second lap will look like rate*1/2 and time *2

r/8*1/2*1/2*2^4+r/8*1/4*1/2*2^5+r/8*1/8*1/2*2^6+r/8*1/2*2^7=2r

so time on the second lap
1/2*2^4+1/2*2^5+1/2*2^6+1/2*2^7=1/2(2^4+2^5+2^6+2^7)=1/2*2^4*15

and time on the first lap
1/2*(1+2^1+2^2+2^3)=1/2*15
dividing 2 time on the first leaves us with 2^4=16
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by iamseer » Sat May 08, 2010 4:59 am
sanju09 wrote: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


I have edited it just once after the first two posts. Can any of iamseer and ansumania tell what I changed there?
You corrected the mistake in typing which you had done. Circumference is 2r and not radius.

Earlier you had mentioned that radius was 2r. Using it answers were not matching any answer options. The distance traveled had to be in terms of pi had the radius been 2r. Also, radius =2r is strange anyways. Then, I assumed you made an error in hurry while typing...took circumference as 2r and solved the question.
"Choose to chance the rapids and dance the tides"
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by sanju09 » Sat May 08, 2010 5:08 am
iamseer wrote:
sanju09 wrote: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


I have edited it just once after the first two posts. Can any of iamseer and ansumania tell what I changed there?
You corrected the mistake in typing which you had done. Circumference is 2r and not radius.

Earlier you had mentioned that radius was 2r. Using it answers were not matching any answer options. The distance traveled had to be in terms of pi had the radius been 2r. Also, radius =2r is strange anyways. Then, I assumed you made an error in hurry while typing...took circumference as 2r and solved the question.
Bingo!! So what's your answer with changed explanation, now?
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by iamseer » Sat May 08, 2010 6:10 am
answer D

the sprinter covers distance r/2 in 30,60,120,240,480..... i.e. time doubling for every next r/2 distance
one round =4*(r/2)

so ratio of time taken for second round to time taken for first round run is
(16+32+64+128)/(1+2+4+8) =16
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by govind_raj_76 » Mon May 10, 2010 7:11 pm
iamseer wrote:answer D

the sprinter covers distance r/2 in 30,60,120,240,480..... i.e. time doubling for every next r/2 distance
one round =4*(r/2)

so ratio of time taken for second round to time taken for first round run is
(16+32+64+128)/(1+2+4+8) =16

Sameer - How did you arrive at the one below ??

(16+32+64+128)/(1+2+4+8) =16
Govind
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by iamseer » Mon May 10, 2010 11:14 pm
govind_raj_76 wrote: Sameer - How did you arrive at the one below ??

(16+32+64+128)/(1+2+4+8) =16
time taken is multiple of 30 for every subsequent distance r/2

first r/2 in 30 seconds
seconds r/2 in 60 seconds
and so on

and one round = 4*(r/2)

HTH!!
"Choose to chance the rapids and dance the tides"
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