Algebra Word Problem

Q:  A bike will overturn if it rounds a corner too sharply or too quickly.  The equation for the max velocity at which a cyclist can turn a corner without tipping over is given by the equation V= 4√(R), where V is the velocity of the bike in miles per hour and R is the radius of the corner in feet.  Find the radius of the sharpest corner that Mandy can safely turn when she rides at a speed of 20 mph.

A:  We have our equation V= 4√(R) and we know that our velocity (V) is 20 mph.  So, plug in 20 for V and solve for R:

V= 4√(R)

20= 4√(R)

Divide both sides by 4

20/4 = 4√(R) / 4

Reduce:

5 = 4√(R) / 4

5 = √(R)

Now, square both sides to solve for R (remember, a square root and a square will cancel each other out):

5² = √(R)²

25 = R

Therefore, the radius of the sharpest turn is 25 feet.