What time is it if the second hand is exactly on a second mark, and exactly 18 second marks ahead of the hour hand?

The angle made by hour hand & seconds hand at any time t seconds is

360*t/(60*60*12) & 360*t/60 respectively

angle between the seconds hand & hour hand is

t*719/120

if seconds hand is on a second mark then t is amultiple of 6 lets say 6*n

if the seconds hand is 18 marks ahead than the angle difference is 108

hence

 n*719/20 = y*360 +108

for it to be possible n has to be a multiple of 20

let us say x*20 therefore

x*719 = y*360 +108

since any number ending in 9 when multiplied with another number will give a number ending in 8 only if the other number ends in 2 & since there are only 60*60*12 seconds in 12 hrs the value of x cannot be more than 360

Trying numbers ending with 2 we get 252 as solution for x

hence t=252*20*6 =30240 seconds

or 8 hrs & 24 mins

 

 

 

Posted by salil on 2006-02-20 07:28:19