4 people can trim a hedge in one hour. How long would it take 3 people? Give your answer in minutes.
Answer (2)
Calculate the work rate of one person: 4 1 hedge per hour.
Calculate the combined work rate of 3 people: 3 × 4 1 = 4 3 hedge per hour.
Calculate the time it takes for 3 people to trim the hedge: 3 4 hours.
Convert the time to minutes: 3 4 × 60 = 80 minutes. The final answer is 80 .
Explanation
Understanding the Problem Let's break down this problem step by step to make sure we understand it clearly. We're given that 4 people can trim a hedge in 1 hour, and we want to find out how long it would take 3 people to trim the same hedge. The key here is to think about the amount of work being done.
Calculating Individual Work Rate First, we need to figure out how much of the hedge one person can trim in one hour. If 4 people can trim the entire hedge in one hour, then one person can trim 4 1 of the hedge in one hour. This is the work rate of one person.
Calculating Combined Work Rate Now that we know one person's work rate, we can find the combined work rate of 3 people. If one person can trim 4 1 of the hedge in an hour, then 3 people can trim 3 × 4 1 = 4 3 of the hedge in one hour.
Calculating Time to Trim the Hedge Next, we need to find out how long it takes for 3 people to trim the entire hedge. If they can trim 4 3 of the hedge in one hour, then the time it takes to trim the entire hedge is the inverse of this fraction, which is 4 3 1 = 3 4 hours.
Converting to Minutes Finally, we need to convert this time from hours to minutes. Since there are 60 minutes in an hour, we multiply 3 4 hours by 60 to get the time in minutes: 3 4 × 60 = 80 minutes.
Final Answer So, it would take 3 people 80 minutes to trim the hedge.
Examples
Imagine you're organizing a team to clean a park. Knowing how quickly a certain number of people can complete a task helps you schedule and allocate resources effectively. For instance, if you know 4 people can clean a section of the park in an hour, you can estimate how long it will take a smaller or larger team to clean the same area. This kind of proportional reasoning is useful in many real-life scenarios, from project management to everyday planning.
Three people will take 80 minutes to trim the hedge if four people can do it in one hour. We calculate this by figuring the work rate of each person, then scaling down for three people and converting the time into minutes. The entire process involves understanding the work rates and combining them effectively.
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