Astudent athlete runs 3 miles in 30 minutes.
a professional runner can run 1 times as far
in 30 minutes. how far can the professional
runner run in 30 minutes?

Each dimension increased by 3.53 ft

Step-by-step explanation:

* Lets explain how to solve the problem

- A rectangular box has dimensions 5 ft by 4 ft by 3 ft

∵ The volume of the rectangular box = l × w × h , where

   l , w , h are its dimensions

∵ l = 5 ft , w = 4 ft , h = 3 ft

∴ Its volume = 5 × 4 × 3 = 60 ft³

- Each dimension of the box is increasing by the same amount

 to yield a new box

- Let each dimension will increase by x ft

∴ The new dimensions are l = (5 + x) , w = (4 + x) , h = (3 + x)

- The volume of the new box is seven times the old

∵ The volume of the old box is 60 ft³

∴ The volume of the new box = 7 × 60 = 420 ft³

∵ The volume of new box = (5 + x)(4 + x)(3 + x)

∴ (5 + x)(4 + x)(3 + x) = 420

- Multiply the 3 brackets

∵ (5 + x)(4 + x) = 20 + 9x + x²

∴ (20 + 9x + x²)(3 + x) = 60 + 47x + 12x² + x³

∴ 60 + 47x + 12x² + x³ = 420

- Subtract 420 from both sides and arrange the terms

∴ x³ + 12x² + 47x - 360 = 0

- Use the ALEKS graphing calculator to find x

∴ x = 3.53

* Each dimension increased by 3.53 ft