If 7 workers can assemble a car in 8 hours, how long would it take 12 workers to assemble the same car?

Options

A. 3 hrs.
B. `3 1//2` hrs.
C. `4 2//3` hrs.
D. `5` hrs.

Answer

To solve the problem of how long it would take 12 workers to assemble a car if 7 workers can do it in 8 hours, we can follow these steps:

### Step 1: Calculate the total work done in worker-hours
First, we need to determine the total amount of work required to assemble the car in terms of worker-hours. If 7 workers can assemble a car in 8 hours, we can calculate the total work as follows:

\[ \text{Total Work} = \text{Number of Workers} \times \text{Time} = 7 \text{ workers} \times 8 \text{ hours} = 56 \text{ worker-hours} \]

### Step 2: Calculate the time taken by 12 workers
Now that we know the total work required is 56 worker-hours, we can find out how long it would take for 12 workers to complete the same amount of work. We can use the formula:

\[ \text{Time} = \frac{\text{Total Work}}{\text{Number of Workers}} = \frac{56 \text{ worker-hours}}{12 \text{ workers}} \]

### Step 3: Simplify the fraction
Now, we simplify the fraction:

\[ \text{Time} = \frac{56}{12} = \frac{14}{3} \text{ hours} \]

### Step 4: Convert to mixed fraction
To express \(\frac{14}{3}\) as a mixed fraction, we divide 14 by 3:

\[ 14 \div 3 = 4 \quad \text{(whole number part)} \]
\[ 14 - (3 \times 4) = 2 \quad \text{(remainder)} \]

Thus, \(\frac{14}{3}\) can be expressed as:

\[ 4 \frac{2}{3} \text{ hours} \]

### Final Answer
Therefore, it would take 12 workers \(4 \frac{2}{3}\) hours to assemble the car.

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