Question

#2 Tire Aspect RatioOn your new small car, you replace the factory-installed P185/75R14 tires with aslightly larger set of tires P205/75R14. Find the circumference of the new tires.(show all work and justify your answer) (8 points)If your odometer reading is 60 miles per hour, your actual speed is how manymiles per hour? (show all work and justify your answer) (6 points)

Answer 1

P205/75R14

Where:

P = passenger tire

205 = tire's width in millimeters

75 = Tire's aspect ratio (height to width) = 0.75 (decimal form)

14 = Diameter of the tire's rim (inches)

So to find the circumference of the new tires:

P205/75R14

Circumference (C)= π x diameter

First, we have to find the Height of the tire:

aspect ratio = height / tire's width

Height = aspect ratio x tire's width

Height = 0.75 x 205 = 153.75 mm

Convert mm into inches;

153.75/25.4 = 6.053 inches

Diameter= Diameter of the rim + 2 ( height of the tire)

D = 14+ 2(6.053) = 26.10 inches

C = π x d = π x 26.10 = 82 inches (circumference of the new tires)

To answer the second part of the question we have to calculate the circumference of the factory-installed tires:

• Factory-installed tires:,P185/75R14

185 = tire's width in millimeters

75 = Tire's aspect ratio (height to width) = 0.75 (decimal form)

14 = Diameter of the tire's rim (inches)

Height of the factory-installed tires:

Height = 0.75 x 185 = 138.75 mm

138.75/25.4 = 5.462 inches

Diameter = 14+ 2(5.462) = 24.92 inches

C = π x d = π x 24.92 = 78.305 inches (circumference of the factory-installed tires)

• Now we have both circumferences:

82 inches (circumference of the new tires)

78.305 inches (circumference of the factory-installed tires)

k =New circumference / factory circumference = 82 / 78.305 = 1.05

After one rotation of the wheel, the newly installed tires will travel 1.05 times further than the factory-installed ones.

So, if the odometer is reading 60 miles per hour, the actual speed is :

60 x k = 60 x 1.05 = 63 miles per hour