Age difference

[cmf2000]

Let's say there are 2 people. The first person is exactly 10 years old when the second person reaches 1 years old. So they have the same birthday. At this point the first person is exactly 10 times the age of the second person. As they both get older the difference in age will always be 10 years but the ratio between ages will get smaller. Can anyone tell me what the equation for this is?
Thanks
Chaz

 

[cmf2000]

"....As they both get older the difference in age will always be 10 years"
You mean 9 years, not 10, right?

Examples (in 4 years, in 24 years):
1, 10 : 10/1 = 10
...
5 14 : 14/5 = 2 4/5
...
25 34 : 34/25 = 1 9/25
...
Can you wrap it up now?

Oh yeah sorry I meant 9 years. I really can't wrap it up lol. I'm in no way a mathematician. My friends were arguing saying there is no equation for that. I was like of course there is but I don't know what it is but I'm going to find out. Thanks

 

[HallsofIvy]

Oh yeah sorry I meant 9 years. I really can't wrap it up lol. I'm in no way a mathematician.

You have a very strange idea as to what kind of problems mathematicians work on! This looks like a seventh or eighth grade arithmetic problem.

My friends were arguing saying there is no equation for that. I was like of course there is but I don't know what it is but I'm going to find out. Thanks

If, at present, t= 0 years, their ages are 1 and 10, then in t years, there ages will be t+ 1 and t+ 10. The ratio (younger over older) will be \(\displaystyle ratio= \dfrac{t+ 1}{t+ 10}\). Notice the "ratio= ". I had to put that in to get an equation. Otherwise it is just \(\displaystyle \dfrac{t+ 1}{t+ 10}\), a ratio, NOT an equation.