The transportation cost charged by a shipping company is proportional to the square root of the distance and proportional to the volume of the parcel. If the distance is increased to 4 times, how much volume of the parcel can be transported with the same cost?
We are given that the cost remains the same (C₁ = C₂) while the distance is increased to 4 times (D₂ = 4D₁). We need to find the new volume (V₂) in terms of the original volume (V₁).
Using the formula:
C₁ = k * √D₁ * V₁
C₂ = k * √D₂ * V₂
Since C₁ = C₂, we have:
k * √D₁ * V₁ = k * √D₂ * V₂
√D₁ * V₁ = √D₂ * V₂
Substitute D₂ = 4D₁:
√D₁ * V₁ = √(4D₁) * V₂
√D₁ * V₁ = 2√D₁ * V₂
Assuming D₁ > 0, we can divide both sides by √D₁:
V₁ = 2 * V₂
Solving for V₂:
V₂ = V₁ / 2
This means the new volume V₂ is half of the original volume V₁, which is 50%.