Final answer:
In mathematics, to calculate how long it will take for 3 people to inflate 4 packs of balloons, you set up a proportion based on the work rates. It will take 3 people a total of 8 hours to inflate 4 packs of balloons.
Step-by-step explanation:
The student is asking about work rate problems, which is a type of problem in mathematics where the rate at which work is done by different parties is used to find out how long it will take them to complete a task together. In this particular case, we are looking to find out how long it will take 3 people to inflate 4 packs of balloons if it takes 2 people 3 hours to inflate one pack.
To solve this, we can set up a proportion based on the work rates. If 2 people can inflate 1 pack in 3 hours, then 1 person can inflate 1 pack in 2 * 3 hours = 6 hours. Therefore, the rate of one person is 1/6 pack per hour.
Since we have 3 people working together, their combined rate is 3 * 1/6 = 1/2 pack per hour, which means they can inflate one pack in 2 hours. As we need them to inflate 4 packs, we would multiply the time to inflate one pack by 4, getting 2 hours * 4 packs = 8 hours for 3 people to inflate 4 packs.