Question

prove that there is no time when the three hands
are equally spaced around the clock

Answer 1

ie the hands are equally \[2\pi/3\] away from each other

Answer 2

hands,A short thick "hour" hand;
A long, thinner "minute" hand;
A very thin "sweep" seconds hand

Answer 3

revolutions made by each hand

hour rev:day 1:12 hours
minute 1:1hour
sweep 1:1 min=1/60hours

Answer 4

let h ,m,s be the angles produced after time t,where t is in hours

Answer 5

i think we can visualise this as a race to cover a straight line of \[2\pi m\]of length

Answer 6

and the speeds of all of them will be 1/12 rev per hour,1 rev per hour,60 rev per hour

Answer 7

at a certain time t they are equally away from each other

Answer 8

so lets say hour hand has already went y meters so since the sweep hand is the largest then the distance covered by each is
s: y+2x=60 rph*t
m: y+x=1 rph*t
h: y=1/12 rph*t

Answer 9

provided they are x meters away from each other

Answer 10

\[2\pi-(2x+y)=x \implies 2\pi=3x+y\\ y=2\pi-3x\]

Answer 11

so
we have to show that there is no such a tym

Answer 12

\[3y+3x=(60+1+\frac{1}{12})t\\6\pi-9x+3x=6\pi-6x=(\frac{733}{12} )t\]
\[t=72\frac{\pi-x}{733} \]

Answer 13

so at @Hero wat time is this...where they are all equal

Answer 14

equally diplaced from each other

Answer 15

http://www.wolframalpha.com/input/?i=solve+%3A+x%282pi%2F60+-+2pi%2F%2860*60%29%29+%3D2*pi%2F3%2C++x%282pi%2F%2860*60%29+-+2pi%2F%2860*60*60%29%29+%3D+2*pi%2F3

Answer 16

one unknown, with two equations, you cant have a solution all the time.

Answer 17

getting delayed for dinner, brb... ive used angular velocity equations in the wolfram solution above...

Answer 18

okay guys let me put the original question

Answer 19

in the original question it says this should be obvius and easy to prove ...this was not the question at hand,i jus wanted to show this easy implicit suppossion

Answer 20

i wanted to prove it

Answer 21

why is @Hero laughin...lol

Answer 22

proof is obvious to see cuz
x = 3
2x = 3

equations will not have a solution

Answer 23

i was concerned wit this part
it is well known,and not difficult to prove, that there is no time when the three hands
are equally spaced around the clock, with each separating angle 2π/3.

Answer 24

did u have a look at wolfram link

Answer 25

let me check it ...

Answer 26

t = time in seconds,


1) angle between seconds, minutes = 2pi/3 :-
t(2pi/60 - 2pi/(60*60)) =2*pi/3 ---------(1)

2) angle between minutes, hours = 2pi/3 :-
t(2pi/(60*60) - 2pi/(60*60*60)) = 2*pi/3 -------(2)

Answer 27

same equation and 60 times of it

Answer 28

there is no solution for above system

Answer 29

okay so thats like the ratio we set up.....okay so we assume there is no solution...for this set,hence no such time exist

Answer 30

wat

Answer 31

when we say there is no solution for below :-
x = 3
2x = 3

are we assuming anything ?

Answer 32

3! or 360! ways to make the pattern?

Answer 33

i need to go, cya

Answer 34

okay,c u later

Answer 35

so now we will consider the original question i will ask in a new slide