...By that reasoning, all the clocks in our cars should be silghtly ahead of the ones in our homes, and should constantly getting farther ahead until we reset them...I'll reach a decision when I check the clock in my car :D
Studies have shown that objects traveling at a faster speed travel further in to the future. For example on the international space station, astronuats are (a really small amount of time ending in a six is all i can remember) ahead of us.
You can demonstrate this to yourself by getting two clocks that are incredibly accurate and can recognize very small amounts of time. Synchronize them, leave one at rest and drive on the highway somewhere with the other one. When you return, the clock you left at rest will be behind the clock you took with you.
EDIT: Don't drive on the high. hehe.