Silverfish and the Clock
Precisely when the big hand of the clock passes 12, Silverfish begins crawling counter clockwise around the clock from the 6 mark at a consistent speed. When reaching the big hand of the clock, the silverfish turns around and at the same speed starts marching around the clock in the opposite direction.
Exactly 45 minutes after the first meeting Silverfish crosses the big hand for the second time and stops. How long was he been crawling?
Exactly 45 minutes after the first meeting Silverfish crosses the big hand for the second time and stops. How long was he been crawling?
posted by Rajesh Lal at
4:58 PM
9 Comments:
well, im sick, can't think, and even add 2+2, but i got first comment!
jerk i wanted that title
that would be 45+45/2=45+22.5=67minitsand 30 seconds
55.9 minutes.
while the big hand travels at 60m/h silver fish travels 105 m/h in order to meet up with the big hand the second time (1 rev.=60min) and cover the 45 minute ground the big hand made while silverfish was going. so... The first meeting would be at:
[60x+105x=30min] or [4x+7x=2][11x=2][x=.181818]
multplying x by 60 to get it in terms of minutes yields 10.9 min
10.9+45=55.9min
Silverfish covers 105 minutes round the clock in the time that the big hand covers 45 minutes. So the speed ratio is 105/45 or 7/3.
Thus, the silverfish advances 7 minutes in the time that the big hand advances 3 minutes, or 21 minutes against 9 minutes when they start 30 minutes apart.
So the total time that the silverfish crawls for is 9 + 45 = 54 minutes.
Chris
it's impossible to know without knowing where silverfish met the big hand on his first trip. you only know silverfish spent 45 minutes getting back around the clock, not how long he spent getting there the first time, or the distance of either trip, simply too many viables missing.
x*(rs+cs)=180; x min to first meeting ; rs is the roach speed in degrees per minute
cs=6 ;clock speed ;6 degrees per min
45 min later, the clock has traveled another 270 degrees
45 min later the roach has traveled the same 270 plus another 360 degrees
in this 45 minutes the roach traveled 630 degrees, or 14 deg per min so rs=14
from the first equation, x = 9 minutes. The clock moved 9 * 6 = 54 degrees and the roach had moved
9 * 14 = 126 degrees at the first meeting.
The answer to how many minutes silverfish was crawing is 9 + 45 = 54 minutes.
hjg
1) why is a silver fish crawling
2) why is something crawling on a clock... and how big is the clock exactly???? for something to take 45 minutes to crawl around a clock.... it must be a prrreettyyy big clock....
3) how is this relevent to life?
-kolohe
how could you know! it does not state the circumfrance of th clock!
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