An electrician can intall 5 light fixtures in 3 hours. Working at that rate, how long will it take the electrician to intall 8 light fixtures?

Options

A. `3(4)/(5)` hours
B. `4(1)/(5)` hours
C. `4(1)/(2)` hours
D. `4(4)/(5)` hours

Answer

To solve the problem step by step, we will use the unitary method to find out how long it will take the electrician to install 8 light fixtures.

### Step 1: Determine the time taken to install one light fixture.
The electrician can install 5 light fixtures in 3 hours. To find the time taken for one light fixture, we divide the total time by the number of fixtures.

\[ \text{Time for one light fixture} = \frac{\text{Total time}}{\text{Number of fixtures}} = \frac{3 \text{ hours}}{5} = \frac{3}{5} \text{ hours} \]

### Step 2: Calculate the time taken to install 8 light fixtures.
Now that we know the time taken for one light fixture, we can find the time taken for 8 light fixtures by multiplying the time for one fixture by 8.

\[ \text{Time for 8 light fixtures} = \text{Time for one light fixture} \times 8 = \frac{3}{5} \text{ hours} \times 8 \]

### Step 3: Perform the multiplication.
Now we multiply:

\[ \frac{3}{5} \times 8 = \frac{3 \times 8}{5} = \frac{24}{5} \text{ hours} \]

### Step 4: Convert the fraction to a mixed number.
To express \(\frac{24}{5}\) as a mixed number, we divide 24 by 5:

\[ 24 \div 5 = 4 \quad \text{(with a remainder of 4)} \]
Thus, \(\frac{24}{5} = 4 \frac{4}{5}\) hours.

### Conclusion:
The time taken by the electrician to install 8 light fixtures is \(4 \frac{4}{5}\) hours.

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