*The Simple Answer to that Question is: 

- 'Quarter' means 1/4 of something 

A quarter of Dollar is worth 25 cents - because A whole Dollar is worth 100 cents  & 1/4 of 100 is 25

And 15 minutes is a quarter of hour because a Whole Hour has 60 minutes - so 1/4 of 60 is 15  :)

🔷 ( Lol, I think I could be a Teacher - I've always had Lots of Patience and I've been Good at Explaining things!  ^_~ 👍 )