Questions: It takes two electricians nine days to rewire 2 identical houses. How long will it take 3 electricians to rewire 3 of the same houses at the same rate?

Solution Steps

To solve this problem, we need to determine the rate at which the electricians work and then use that rate to find out how long it will take a different number of electricians to complete a different number of houses.

1. Calculate the rate at which the two electricians work together.
2. Use this rate to determine the time it would take for three electricians to rewire three houses.

Given:

• \(2\) electricians
• \(9\) days
• \(2\) houses

The rate at which the two electricians work together is: \[ \text{Rate per day} = \frac{\text{houses}}{\text{days}} = \frac{2}{9} \approx 0.2222 \text{ houses/day} \]

The rate per electrician is: \[ \text{Rate per electrician} = \frac{\text{Rate per day}}{\text{number of electricians}} = \frac{0.2222}{2} \approx 0.1111 \text{ houses/day} \]

Given:

• \(3\) electricians

The total rate for three electricians is: \[ \text{Total rate for 3 electricians} = \text{Rate per electrician} \times \text{number of electricians} = 0.1111 \times 3 \approx 0.3333 \text{ houses/day} \]

Given:

• \(3\) houses

The time it will take for three electricians to rewire three houses is: \[ \text{Time} = \frac{\text{houses}}{\text{total rate}} = \frac{3}{0.3333} \approx 9.0 \text{ days} \]

Final Answer