Running at Different Speeds: Who Experiences Time Differently?

[Hepic]

Lets say we run(forever) with 200km/h and our friend with 10km/h.
Time will run slower for me or will run faster for my friend?

 

[Doc Al]

Lets say we run(forever) with 200km/h and our friend with 10km/h.

Those speeds are with respect to what? For example: You run eastward at 200 km/h with respect to the ground and your friend runs westward at 10 km/h with respect to the ground.

Time will run slower for me or will run faster for my friend?

"Time" is relative. You think your clocks (and everything else moving along with you) are running at their normal rates. But you say that your friends clocks are running slow compared to yours.

Of course, it's completely symmetrical. Your friend says the same thing about your clocks running slow.

 

[Hepic]

If I run faster I will see my friends clock go slower,and my friend will see my clock to go faster?

 

[Doc Al]

If I run faster I will see my friends clock go slower,and my friend will see my clock to go faster?

No. You both see each others clocks as running slow.

 

[Hepic]

Ohh why? I thought the faster you run the slower time.
Why the slower person see the time of faster person with slower from his time?

 

[Doc Al]

Ohh why? I thought the faster you run the slower time.

Only as seen by someone else, not by you. As far as you are concerned, your clocks run normally.

Why the slower person see the time of faster person with slower from his time?

Time dilation is one of the consequences of relativity. It is derived, like everything else, from Einstein's postulates: the laws of physics are the same in every inertial frame and the speed of light is the same in every inertial frame.

Since you're obviously interested in relativity, I recommend you get yourself a good tutorial book and work through it, step by step.