I'm not quite sure about 3 miles, but I'm 14 and can run a mile in 6 minutes and 33 seconds.
im 13 and i have a 5 k time (3.1 miles) of 20:10. the average 3 mile time for a 13 year old might be 25 - 30 minutes
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20-25 minutes.
I am 30 now but when I was in high school at 15. I was pretty average. average height weight build leg length etc.
21-22 minutes as I recall was roughly my times for 2.5 miles so 4.25 to 4.4 per mile allow for slow due to longer run say 4.6 minutes so your looking at 26 minutes.
There will be many things that will affect your time such as when you ate and what you ate.
weather ie: cold weather is better as heat tires you more, but icey air hurts the throat and ice under foot will slow you alot. The course: a running track is flat and easy, but psycologically being able to break a long run down into small acheivable targets makes it easier. What you wear. your size including leg length and lung size.
But most of all how much exercise you take. I used a bike as my main transport and would think nothing of riding 10 miles or walking from 9am to 7pm. This was compensated by the fact I smoked.
If you wish to improve your fitness Start slowly, I cannot express how important stretching is. injury is easily caused by not stretching or by pushing yourself too hard. You won't get better having to rest an injury as most injuries need rest to heal.