It takes 6 workers 8 hours to transfer 400 bales of hay. With an extra 2 workers, how long would it take to transfer 600 bales

We can solve this problem using the concept of **work rate**. Here's a step-by-step breakdown of the solution:

### Step 1: Calculate the work rate of the 6 workers.
- The total work is to transfer **400 bales** in **8 hours** with **6 workers**.
- Work rate of the 6 workers combined = \( \frac{400 \text{ bales}}{8 \text{ hours}} = 50 \text{ bales per hour} \).

Since this is the rate for 6 workers, the work rate of **1 worker** is:
\[
\frac{50 \text{ bales per hour}}{6} \approx 8.33 \text{ bales per hour per worker}.
\]

### Step 2: Calculate the work rate of 8 workers.
If 1 worker transfers 8.33 bales per hour, the rate for **8 workers** (6 original workers + 2 extra workers) is:
\[
8 \times 8.33 = 66.64 \text{ bales per hour}.
\]

### Step 3: Calculate the time needed to transfer 600 bales with 8 workers.
- Total work = 600 bales
- Work rate of 8 workers = 66.64 bales per hour

Time required = \( \frac{600 \text{ bales}}{66.64 \text{ bales per hour}} \approx 9 \) hours.

### Final Answer:
With 8 workers, it will take approximately **9 hours** to transfer 600 bales of hay.

Would you like further details or have any questions?

Here are some related questions to consider:
1. What happens if we reduce the number of workers to 4?
2. How would the time change if we need to transfer 800 bales instead of 600?
3. How does the time vary if the workers work faster or slower?
4. What if the extra workers are less efficient than the original ones?
5. How does the overall time change if breaks are included?

**Tip**: When dealing with such problems, it's important to understand the relationship between the number of workers, the work rate, and the total time taken.

It takes 6 workers 8 hours to transfer 400 bales of hay. With an extra 2 workers, how long would it take to transfer 600 bales?

Explore how to calculate the time required to transfer hay bales with extra workers using work rate and proportional reasoning. Learn step-by-step calculations to solve this problem, making it ideal for middle school students studying rates and ratios.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation