 if 3 people can wash a car in 8hr, the number of cars 6 people can wash in 12 hr is?

To solve this problem, we can use the concept of work rates. Here's how you can approach it:

1. **Determine the work rate of 3 people:**
   - If 3 people can wash 1 car in 8 hours, their work rate is:
   \[
   \text{Work rate of 3 people} = \frac{1 \text{ car}}{8 \text{ hours}} = \frac{1}{8} \text{ cars per hour}
   \]

2. **Find the work rate of 1 person:**
   - Since 3 people have a combined work rate of \(\frac{1}{8}\) cars per hour, the work rate of 1 person is:
   \[
   \text{Work rate of 1 person} = \frac{1}{3} \times \frac{1}{8} = \frac{1}{24} \text{ cars per hour}
   \]

3. **Determine the work rate of 6 people:**
   - The work rate of 6 people would be 6 times the work rate of 1 person:
   \[
   \text{Work rate of 6 people} = 6 \times \frac{1}{24} = \frac{6}{24} = \frac{1}{4} \text{ cars per hour}
   \]

4. **Calculate the number of cars washed by 6 people in 12 hours:**
   - If 6 people work for 12 hours, the number of cars they can wash is:
   \[
   \text{Number of cars} = \text{Work rate of 6 people} \times \text{Time} = \frac{1}{4} \text{ cars per hour} \times 12 \text{ hours} = 3 \text{ cars}
   \]

Thus, **6 people can wash 3 cars in 12 hours**.

Would you like more details on any part of this solution? Here are some related questions to deepen your understanding:

1. How would the solution change if the number of hours increased to 16?
2. What if only 2 people were washing the cars for 12 hours?
3. How many cars could 9 people wash in 8 hours?
4. How long would it take 4 people to wash 5 cars?
5. If 6 people started washing cars but lost 2 workers after 6 hours, how many cars would they complete in 12 hours?

**Tip:** When dealing with work rate problems, it's helpful to break down the rate per individual and then scale up based on the number of workers and hours.

If 3 people can wash a car in 8 hours, how many cars can 6 people wash in 12 hours?

Learn how to calculate the number of cars that 6 people can wash in 12 hours using work rate concepts. This problem covers essential mathematical ideas, including work rate and proportions. Suitable for students in Grades 5-7.

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