three people working together can unload a truck in 2 hours. if 12 trucks must be unloaded within 8 hours how many people should be assigned to this job?

We can solve this problem by first calculating the rate at which three people unload one truck, then determining the total work required, and finally calculating how many people are needed to meet the time constraint.

### Step 1: Rate of 3 people unloading one truck
Three people can unload one truck in 2 hours, so the rate at which they work together is:
\[
\text{Rate of 3 people} = \frac{1 \, \text{truck}}{2 \, \text{hours}} = 0.5 \, \text{trucks per hour}
\]

Since this is the rate for 3 people, the rate per person is:
\[
\text{Rate per person} = \frac{0.5 \, \text{trucks per hour}}{3} = \frac{1}{6} \, \text{trucks per person per hour}
\]

### Step 2: Total work required
There are 12 trucks that must be unloaded within 8 hours, so the total amount of work is:
\[
\text{Total work} = \frac{12 \, \text{trucks}}{8 \, \text{hours}} = 1.5 \, \text{trucks per hour}
\]

### Step 3: Number of people needed
We know each person can unload \( \frac{1}{6} \) trucks per hour. To unload 1.5 trucks per hour, the number of people needed is:
\[
\text{Number of people} = \frac{1.5 \, \text{trucks per hour}}{\frac{1}{6} \, \text{trucks per person per hour}} = 1.5 \times 6 = 9
\]

### Final Answer:
To unload 12 trucks in 8 hours, 9 people should be assigned to this job.

Would you like further clarification on any part of this solution?

### Related Questions:
1. What if 10 trucks had to be unloaded in 6 hours?
2. How would the number of people change if the unloading time per truck was 3 hours?
3. How many trucks could 5 people unload in 8 hours?
4. What if each person could unload 1 truck in 3 hours instead?
5. How many people would be required to unload 20 trucks in 5 hours?

### Tip:
When solving rate problems, always break the problem down into "work per time" to find how much work each person or group can complete per hour or minute.

Three people working together can unload a truck in 2 hours. If 12 trucks must be unloaded within 8 hours, how many people should be assigned to this job?

Solve a practical work and time problem where three people can unload a truck in 2 hours. Find out how many people are needed to unload 12 trucks in 8 hours using rates and proportional reasoning. This step-by-step solution is perfect for students in Grades 6-8.

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