On occasion, we have one problem for a homework assignment. These problems are generally hard. This one in particular is giving me a difficult time...
Here it is:
A new game is set to revolutionize the gaming industry. In this game, two players enter a contest field. The players are placed 500 feet apart. Just behind each player is a large wall that moves in as the game progresses. The wall on the left side moves in at a rate of 1 mph, while the wall on the right moves in at a rate of 1.5 mph.
The challenge of the game is to complete a guaranteed number of throws back and forth, between the players, before the moving walls reach a distance of 30 feet apart, at which point they instantaneously squash anything between them.
The game begins when the two individuals enter the field of play. One is given a ball and asked to make a guarantee as to the number of completed throws. If the players make their guaranteed number of tosses then they are awarded one point for each completed toss. If they fail to make the guarantee before the walls come together, then lets just say that a player never loses as second game of.
Let's get to the specifics. First, we will assume that it takes 2 seconds for a player to catch and throw a ball. Player one can throw at 50 mph. Player 2 can throw at 60 mph.
How many completed throws should our participants guarantee to ensure their safety, as well as their hightest possible score? Is there an advantage to placing each player next to the left or right wall? Also, which player should start with the ball?
*Clock starts at release of the first ball
*The players are at the walls; there is no distance between each player and their wall
I've read and reread the problem several times. I've decided that first I have to find how much time it takes for the walls to get to 30 ft apart. I converted the speeds of the walls into ft per second and then multiplied each by "x" and then I multiplied these products together. Then I divided 470 by the product to get the number of seconds it takes for the walls to reach 30 feet. Was this a viable method? What should I do now?
Thank you!
Here it is:
A new game is set to revolutionize the gaming industry. In this game, two players enter a contest field. The players are placed 500 feet apart. Just behind each player is a large wall that moves in as the game progresses. The wall on the left side moves in at a rate of 1 mph, while the wall on the right moves in at a rate of 1.5 mph.
The challenge of the game is to complete a guaranteed number of throws back and forth, between the players, before the moving walls reach a distance of 30 feet apart, at which point they instantaneously squash anything between them.
The game begins when the two individuals enter the field of play. One is given a ball and asked to make a guarantee as to the number of completed throws. If the players make their guaranteed number of tosses then they are awarded one point for each completed toss. If they fail to make the guarantee before the walls come together, then lets just say that a player never loses as second game of.
Let's get to the specifics. First, we will assume that it takes 2 seconds for a player to catch and throw a ball. Player one can throw at 50 mph. Player 2 can throw at 60 mph.
How many completed throws should our participants guarantee to ensure their safety, as well as their hightest possible score? Is there an advantage to placing each player next to the left or right wall? Also, which player should start with the ball?
*Clock starts at release of the first ball
*The players are at the walls; there is no distance between each player and their wall
I've read and reread the problem several times. I've decided that first I have to find how much time it takes for the walls to get to 30 ft apart. I converted the speeds of the walls into ft per second and then multiplied each by "x" and then I multiplied these products together. Then I divided 470 by the product to get the number of seconds it takes for the walls to reach 30 feet. Was this a viable method? What should I do now?
Thank you!