Which company is more productive overall and by how much (use percentage)?

Steps to Solve

1. Calculate the productivity for Company A To find the productivity of Company A, we divide the total miles paved by the total cost.

Let:

• Total miles paved by Company A = 3 miles
• Total cost for Company A = $12,000

Productivity for Company A:

$$ \text{Productivity}_A = \frac{\text{Miles}_A}{\text{Cost}_A} = \frac{3 \text{ miles}}{12000 \text{ dollars}} = \frac{1}{4000} \text{ miles per dollar} $$

2. Calculate the productivity for Company B Now, we repeat the process for Company B.

Let:

• Total miles paved by Company B = 5 miles
• Total cost for Company B = $15,000

Productivity for Company B:

$$ \text{Productivity}_B = \frac{\text{Miles}_B}{\text{Cost}_B} = \frac{5 \text{ miles}}{15000 \text{ dollars}} = \frac{1}{3000} \text{ miles per dollar} $$

3. Compare the productivities Next, we need to see which company is more productive. We can compare $\text{Productivity}_A$ and $\text{Productivity}_B$.

4. Calculate the percentage increase To find out how much more productive Company B is compared to Company A, we will use the formula for percentage increase:

$$ \text{Percentage Increase} = \left( \frac{\text{Productivity}_B - \text{Productivity}_A}{\text{Productivity}_A} \right) \times 100 $$

Using our previously calculated productivities,

$$ \text{Percentage Increase} = \left( \frac{\frac{1}{3000} - \frac{1}{4000}}{\frac{1}{4000}} \right) \times 100 $$

5. Simplify and solve the percentage increase Calculating the difference in productivities and finding the percentage gives:

$$ \text{Productivity}_A = \frac{1}{4000} = 0.00025, $$ $$ \text{Productivity}_B = \frac{1}{3000} \approx 0.0003333. $$

Calculating the percentage:

$$ \text{Percentage Increase} = \left( \frac{0.0003333 - 0.00025}{0.00025} \right) \times 100 \approx 33.33% $$