Identifying the Rate of Filling Bins

Oct 13, 2025 by windailys.com 65 views

Understanding the Problem

The problem presents a scenario where a farmer fills bins of corn at a certain rate. We are given that the farmer takes 1 week to fill 9 bins of corn. The task is to determine how long it will take for the farmer to fill 450 bins at the same rate.

Identifying the Rate of Filling Bins

To solve this problem, we need to identify the rate at which the farmer fills the bins. The rate can be calculated by dividing the number of bins filled by the time taken to fill those bins. In this case, the farmer fills 9 bins in 1 week.

Calculating the Rate of Filling Bins

The rate of filling bins can be calculated as follows:

Rate = Number of bins filled / Time taken to fill those bins Rate = 9 bins / 1 week Rate = 9 bins/week

Applying the Rate to Fill 450 Bins

Now that we have the rate at which the farmer fills the bins, we can use it to determine how long it will take to fill 450 bins. We can set up a proportion to relate the number of bins filled to the time taken to fill those bins.

Setting Up a Proportion

Let's set up a proportion to relate the number of bins filled to the time taken to fill those bins:

9 bins / 1 week = 450 bins / x weeks

Solving for x

To solve for x, we can cross-multiply the proportion:

9x = 450 * 1 9x = 450 x = 450 / 9 x = 50

Conclusion

Therefore, it will take the farmer 50 weeks to fill 450 bins at the same rate.

Real-World Applications

This problem has real-world applications in various fields, such as agriculture, manufacturing, and logistics. Understanding the rate at which a task is performed is crucial in planning and managing resources.

Tips and Tricks

When solving problems involving rates and proportions, it's essential to:

Identify the rate at which the task is performed
Set up a proportion to relate the number of units to the time taken
Solve for the unknown variable
Check the solution to ensure it makes sense in the context of the problem

Practice Problems

Try solving the following problems:

A machine produces 12 units per hour. How long will it take to produce 240 units at the same rate?
A farmer takes 2 days to fill 12 bins of corn. At this rate, how long will it take to fill 300 bins?

Conclusion

In conclusion, the problem of determining how long it will take to fill 450 bins at a given rate is a classic example of a proportion problem. By identifying the rate at which the task is performed and setting up a proportion, we can solve for the unknown variable and determine the time required to complete the task.

Q: What is the rate at which the farmer fills the bins?

A: The rate at which the farmer fills the bins is 9 bins per week.

Q: How can we calculate the rate of filling bins?

A: We can calculate the rate of filling bins by dividing the number of bins filled by the time taken to fill those bins. In this case, the farmer fills 9 bins in 1 week, so the rate is 9 bins/week.

Q: How can we use the rate to determine how long it will take to fill 450 bins?

A: We can set up a proportion to relate the number of bins filled to the time taken to fill those bins. The proportion is:

9 bins / 1 week = 450 bins / x weeks

Q: How do we solve for x in the proportion?

A: To solve for x, we can cross-multiply the proportion:

9x = 450 * 1 9x = 450 x = 450 / 9 x = 50

Q: What does the solution x = 50 mean?

A: The solution x = 50 means that it will take the farmer 50 weeks to fill 450 bins at the same rate.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields, such as agriculture, manufacturing, and logistics. Understanding the rate at which a task is performed is crucial in planning and managing resources.

Q: What are some tips and tricks for solving problems involving rates and proportions?

A: When solving problems involving rates and proportions, it's essential to:

Identify the rate at which the task is performed
Set up a proportion to relate the number of units to the time taken
Solve for the unknown variable
Check the solution to ensure it makes sense in the context of the problem

Q: Can you provide some practice problems for readers to try?

A: Here are some practice problems:

A machine produces 12 units per hour. How long will it take to produce 240 units at the same rate?
A farmer takes 2 days to fill 12 bins of corn. At this rate, how long will it take to fill 300 bins?

Q: What is the most important thing to remember when solving problems involving rates and proportions?

A: The most important thing to remember is to identify the rate at which the task is performed and set up a proportion to relate the number of units to the time taken.

Q: Can you provide some additional resources for readers who want to learn more about rates and proportions?

A: Here are some additional resources:

Khan Academy: Rates and Proportions
Mathway: Rates and Proportions
IXL: Rates and Proportions

Q: What is the final answer to the original problem?

A: The final answer to the original problem is 50 weeks. It will take the farmer 50 weeks to fill 450 bins at the same rate.