In a game of tug-of-war, a team wins by pulling the ﬂag over its goal line. The ﬂag begins at 0. During a game, the ﬂag moves 8 feet to the right, 12 feet to the left, and 13 feet back to the right. Did a team win? Explain
Think of the flag as 0 on a number line. Move to the right is positive, move to the left is negative...
We begin on 0 and move 8 feet to the right. Now we move 12 feet to the left... 8 - 12 = -4. We are at -4 on the number line. Now we move back to the right 13 feet... -4 + 13 = 9. We are at 9 on the number line.
So did any team win? It depends on how far the goal line is from zero. We know that it's farther than 8 feet from zero because they didn't call the game after the first 8 feet. When it went back to the left it only went 4 feet from zero. When it goes back to the right, it is now 9 feet from zero. If the goal line is 9 feet or less from zero then one of the teams win... but if the goal line is greater than 9 feet from 0, no team wins (because nobody went that far).
Don't worry... I'm sure that both teams got a participation ribbon. . .