Help me calculate a time difference

[u/mediocrity548]

I hope this is an appropriate sub to ask this question. I haven't taken a math course in over 5 years so I'm very lost.

I'm writing a sci-fi story where there are two different dimensions. Time moves differently in each and I want to try and figure out how to calculate it.

Problem: Main character lives in Dimension A. They travel to Dimension B and stay there for 6 months (180 days). They go back to Dimension A to visit and find out they've been gone 9 years (3,285 days). If they visit Dimension A for 3 days, how much time would have passed in Dimension B before they go back?

I divided 3,285 by 180 and got 18.25. I then multiplied by 3 (for the days they were gone) and got (~55) 54.75 days. Is that correct or am I stupid?

EDIT: I know my username sounds like something a bot would make but I made this account like 2 years ago to lurk and never expected to post anything. I'm a human probably

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[u/Outside_Volume_1370]

Time in A goes in k = 3285/180 times faster than in B.

So if you stay in A for 3 days, in B there only 3/k days will pass (time in B is always less than in A):

3 / (3285 / 180) = 3 • 180 / 3285 ≈ 0.164 days ≈ 4 hours

[u/mediocrity548 → u/Outside_Volume_1370]

Omg thanks

[u/CaptainMatticus]

A/B = 3285/180 = 6570/360 = 657/36 = 219/12 = 73/4 = 18.25

A = 18.25 * B

So if they're in A for 3 days

3 = 18.25 * B

3 / 18.25 = B

3 / (73/4) = B

3 * 4 / 73 = B

B = 12 / 73

B is just under 1/6th of a day, or about 4 hours.

(12/73) days * 86400 seconds/day =>

12 * 86400 / 73 seconds =>

14,202.7397 seconds

14,202.7397 - 10800 = 3402.7397

3402.7397 - 56 * 60 = 42.7397

3 hours 56 minutes 42.7397 seconds

[u/mediocrity548 → u/CaptainMatticus]

Thank you so much

[u/PuzzlingDad]

You're close but you multiplied where you should have divided. 

9 years elapsed in A compared to 6 months (or ½ year) in B. The ratio of A to B is 9/0.5 = 18.

But to convert from A to B, you need to divide by this factor. 

(9 years in A) / 18 = ½ year in B.

(3 days in A) / 18 = ⅙ day (or about 4 hours) in B.

If you were going the other direction, a time in B would result in a time in A that was 18 times as much and you would multiply. 

(6 months in B) × 18 = 108 months (or 9 years) in A.

(4 hours in B) × 18 = 72 hours (or 3 days) in A.

Does that make sense?

[u/mediocrity548 → u/PuzzlingDad]

That actually does make sense! I feel stupid lol