Question

Please help me if you can

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:

`t=5.825\sqrt[3]{w/p}`

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.

Two students solved this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. Why was Daniel wrong? Show each step that led Daniel to the wrong answer

Answer 1

Explanation:

Plug in known values

`13.4 = 5.825\sqrt[3]{(3590)/(p)}\\`

Divide both sides by 5.825

`2.3004 = \sqrt[3]{(3590)/(P)}\\`
Cube both sides

`12.1738 = (3590)/(P)`

Multiply both sides by P

`12.1738P = 3590`

Divide both sides by 12.1738

`P = 294.895`

Round to nearest hp

`P = 295`

So if you look at the radical, it's possible for it to be mistake for a square root, and not a cube root. This was Daniels mistake, so his steps were

`13.4 = 5.825\sqrt[3]{(3590)/(p)}\\`

Divide both sides by 5.825

`2.3004 = \sqrt[3]{(3590)/(P)}\\`

Square both sides

`5.29197 = (3590)/(P)`

Multiply both sides by P

`5.29197P = 3590`

Divide both sides by 5.29197

`p\approx 678.385`

He also probably rounded during his steps, which would explain how he got 679 instead of 678 when rounding in the final, but either way his answer is completely off, and this is due to him mistakenly thinking the cube root was a square root.