With 1,7,49
We get
J/K = (F-1/S)/(F-1/M) = 8/7
So K=7
T=KFM/2(M-F) = 49/12 = 4 1/12
After 1T , the planes have gone 4+1/12,1/2+1/12,1/12 so they are lined up FSXM
After 2T they have gone twice that, 8+1/6,1+1/6,1/6 so they are FMSX
I mean the periods of the planets are 1, pi, and e, where pi and e are the fundamental constants. i.e the periods of the planets are 1 year, about 2.718 years, and about 3.14 years. When will they next all be in line with the sun?
@forkedknightsaid Since J / K must be rational they will never align
Well spotted .
Pi and Eulers constant
I'll try to get a life instead of trying to find simple equations where non exist.
I've enjoyed these discussions and hope I've learned something!!
All the other problems in my old book are far too easy because even I can do them!!
@vendasaid Well spotted .
Pi and Eulers constant
I'll try to get a life instead of trying to find simple equations where non exist.
I've enjoyed these discussions and hope I've learned something!!
All the other problems in my old book are far too easy because even I can do them!!
Sometimes in math you just need to know the bridge.
I am guessing these formulas assume speed is constant.
If the last problem was based on a circle, seems to me the arc tangents being equal would be a nice generalization.
Here is a nice puzzle for those who do not know how to approach it. If Keven can do a job in 5 hours and Larry can do the same job in 3 hours, how long will it take them to do the job working together?
@eladarsaid Here is a nice puzzle for those who do not know how to approach it. If Keven can do a job in 5 hours and Larry can do the same job in 3 hours, how long will it take them to do the job working together?
That depends heavily on how much the job can be parallelized. Are you assuming 100%?
@eladarsaid Here is a nice puzzle for those who do not know how to approach it. If Keven can do a job in 5 hours and Larry can do the same job in 3 hours, how long will it take them to do the job working together?
Approximately 1 hour and 53 minutes. Keven does 0.333 percent of the job each minute and Larry does 0.555 percent each minute. Together they complete 0.888 per cent per minute. The total job is finished after 112.6 minutes, or 1 hour and 53 minutes (minus a few seconds).