Please help. mr trocki is the groundskeeper for a vacation resort. he has programmed the sprinkler system to run at night in three different zones. The sprinklers turn on at midnight and run until 7am. the fist zone runs every 90 minutes, the second zone turns on every 40 minutes, and the third zone turns on every 45 minutes. write a word problem within the context of the vacation resort that can be solved by determining the GCF
One hot summer day, a group of guests at the vacation resort are enjoying a game of beach volleyball. They want to take turns cooling off in the sprinklers between each set, but they're concerned about being interrupted by the sprinkler system. To plan their breaks accordingly, they want to find out the shortest amount of time they can play without worrying about getting wet.
To solve this problem, we need to determine the Greatest Common Factor (GCF) of the intervals between each instance of the sprinklers turning on in all the zones. The GCF will give us the length of time after which all the zones will align and the sprinklers won't interrupt the game.
The intervals between the sprinklers in each zone are as follows:
- Zone 1: 90 minutes
- Zone 2: 40 minutes
- Zone 3: 45 minutes
To find the GCF, we can observe the common factors of all three numbers and identify the greatest one. In this case, the common factors are 1 and 5. However, since we're looking for the shortest amount of time, we can ignore the 5 because it will result in a longer duration.
Next, we need to find the GCF of the remaining numbers, which are 1, 3, and 9. The greatest common factor among these numbers is 1.
Therefore, the GCF of the intervals between the sprinklers in all three zones is 1. This means that every minute, there is a possibility of the sprinklers turning on in some zone. Consequently, the guests cannot play for more than a minute without the risk of getting wet during their game of volleyball.