Loading...
Boppo is a game played by 2 teams for a fixed duration (number of minutes). It is played with 8 members of each team on the floor—actually playing the game—at all times. At any time during the game, exactly one player from each team must be off the floor—not actually playing. Thus by taking a break, by entering the game after it starts, or by leaving before it finishes, every player on each team must spend exactly 5 minutes resting or otherwise not playing.
In the table, identify a number of players per team and a number of minutes per game that are consistent with the given information about Boppo. Make only two selections, one in each column.
9
11
18
30
45
50
Let's create a timeline to understand the player rotation:
Game Timeline (M minutes) |-------------------------------------------------------| 8 on floor + 1 off floor (continuously throughout game) Player perspective: Each player: [---Playing (M-5 minutes)---][Rest 5 min]
We need to find values that work together:
Let's think about total rest time from two perspectives:
From game perspective:
From players perspective:
These must be equal: \(\mathrm{P} \times 5 = \mathrm{M}\)
This means:
Let's check our answer choices systematically:
Checking if choices can be number of players (P):
Checking if choices can be game duration (M):
? Stop here - we found our answer.
With 9 players and 45-minute game:
Number of players per team: 9
Number of minutes per game: 45
These values satisfy all constraints: with 9 players per team and a 45-minute game, exactly 1 player can rest at all times while 8 play, and each player gets exactly 5 minutes of rest.