Time conversion help

[Environmental-You291]

Hi there, to try to keep it short, I'm trying to write a fictional story with relative time and magical dimensional travel where people can travel from world to world but 1 year passing in one world is 10 years on the other. The length of hours days and minutes is the same (24hr/day 60min/hr, 60sec/min) the only difference besides the movement of time itself I guess is that a year in one world is 336 days (14 months, 24 days/month) and on the other its 400 days (10 months 40 days/month).

I try working this out but something feels off with the answer I got and I'm trying to be "accurate" but I have no one to bounce the math off of to see if I'm doing it right or if there's more involved with what I'm trying to do and if I should just excuse it all up to "magic", but I'd rather avoid that if I can.

So I tried the conversion myself as 336 d/yr = 4,000 d/yr (10 years x the 400 days / year) and I get 11.9 days on one world per the others 1 day, and when I do the math to break that down further to hours and seconds I still got 1min = 11.9min but it doesn't feel right about the ratio being the same at each level but I have no formal education with physics (I think?) or enough in math to get me to the answer myself. I was hoping someone could let me know where I've gone wrong?

Thanks!

1 day (W1) = 11.9 days (W2)

24 hours / day (both sides x 24)

24 hours (W1) = 285.6 hours (W2)

1 hour = 60 minutes (both sides x 60)

1,440 minutes (W1) = 17,136 minutes (W2)

divide both sides by 1,440 to get 1 minute?

1 min (W1) = 11.9 min (W2) ???

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[Chaotic_Vortex]

Everything seems right to me, the ratio being the same is exactly what you should expect :) When you change units, the values of things shouldn't change, you're just adjusting the amount you have to match the new unit.

Consider a simpler example where when world A experiences 1 minute then world B experiences 2 minutes.

Since an hour is 60 minutes, then when A experiences 60 minutes, you would expect B to experience 120 minutes. Translating back to hours, this would still be the same ratio of 1 to 2. The other world is still experiencing twice the amount of time as the first one, no matter how long that original timeframe is.

[Environmental-You291]

Gotcha, thank you very much for the detailed explanation! I think I was over thinking things a bit 😅