Question

5. The rear wheels of DeMarius' car complete 4/5 of a rotation for every full rotation of a front wheel. What is the

radius, in feet, of a rear wheel on the car? Write your answer as a simplified fraction.

Answer 1

To find the radius of the rear wheel, we can set up a ratio using the information given in the question and the circumference formula. However, the question does not provide the radius of the front wheel, so we cannot determine the exact value of the rear wheel's radius. The radius of the rear wheel would be 4/5 times the radius of the front wheel, or 4R/5.

Step-by-step explanation:

To find the radius of the rear wheel on DeMarius' car, we can set up a ratio using the information given in the question. The ratio is 4/5, meaning that for every 4/5 of a rotation of the rear wheel, the front wheel completes one full rotation. Let's call the radius of the rear wheel 'r'. Since the front wheel completes one full rotation, the circumference of the front wheel is 2π times the radius of the front wheel. Similarly, the circumference of the rear wheel is 2π times the radius of the rear wheel. Using the ratio and the circumference formula, we can set up the following equation: 2πr / (2πR) = 4/5, where 'R' is the radius of the front wheel.

Now, we can simplify the equation by canceling out the 2π terms:

r / R = 4/5.

To find the value of 'r', we need to know the radius of the front wheel, 'R'. Unfortunately, the question does not provide this information, so we cannot determine the exact value of 'r'. However, we know that the answer should be written as a simplified fraction. So, the radius of the rear wheel would be 4/5 times the radius of the front wheel, or 4R/5.