Radical Equations

Question

Introduction

The time, t in seconds that it takes a car to travel a quarter-mile when starting from a full stop can be estimated by using the formula:

Where w = weight of the car

            p = power delivered by the engine in horsepower (hp)

If the quarter-mile time for a 3,590-pound car is 13.4 s, how much power does its engine deliver? Round to the nearest pound.

Assignment

Natasha and Daniel worked out this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. 

1. Who was right?
2. How did you determine who was right? Show each step of how each of them solved the problem.
3. Set up your Fantasy Race. Research two different cars/trucks. What is the average hp and weight of each? Based on the formula, how fast can each reach a quarter-mile? Show all the work for each.

Answer 1

From the internet, the equation for this problem is likely t = 5.825 times the cubed root of (w/p). Plug in the given values for t and w into the cubed root equation.

13.4 = 5.825 times the cubed root of (3590/p) or 5.825 (3590/p)^1/3

Solve for p.

Divide both sides of the equation by 5.825 which gives you

2.304 = (3590/p)^1/3

Next, cubing both sides of the equation will eliminate the radical and give you

2.304³ = ((3590/p)^1/3)³ or 12.174 = 3590/p

Solve for p. p = 294.89 or approximately 295 hp. Natasha’s answer is correct.

Daniel’s answer is the result of using a square root instead of the cubed root.