Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Janessa recently increased the size of his Jeep tires from the original P230/85R18 to the larger P250/85R21. If Janessa didn’t recalibrate her odometer, how far did she really travel on the new tires when her odometer shows she has traveled 23425 miles?


Sagot :

onyebuchinnaji

The distance Janessa traveled on the new tires with the given size is 26,470.25 miles.

The given parameters:

  • Original size of the tire, = P230/85R18
  • The width of the smaller tire, = 230 mm
  • Aspect ratio, = 85%
  • Larger size of the tire, = P250/85R21
  • The width of the larger tire, = 250 mm
  • Aspect ratio, = 85%
  • Reading of the odometer = 23,425 miles

The diameter of the smaller tire is calculated as follows;

[tex]0.85 = \frac{h}{230} \\\\h = 0.85 \times 230 \\\\h = 195.5 \ mm\\\\h = 195.5 \ mm \times \frac{1 \ in}{25.4 \ mm} \\\\h = 7.7 \ in[/tex]

diameter of the smaller tire;

D = 2(7.7 in)  + 18 in

D =  33.4 in

The circumference of the smaller tire;

[tex]C_1 = \pi D\\\\C_1 = 3.142 \times 33.4 \\\\C_1 = 104.94 \ in[/tex]

The diameter of the larger tire is calculated as follows;

[tex]0.85 = \frac{h}{250} \\\\h = 0.85 \times 250 \\\\h = 212.5 \ mm\\\\h = 212.5 \ mm \times \frac{1 \ in}{25.4 \ mm} \\\\h = 8.37 \ in[/tex]

diameter of the larger tire;

D = 2(8.37 in)  + 21 in

D =  37.74 in

The circumference of the larger tire;

[tex]C_2 = \pi D\\\\C_2 = 3.142 \times 37.74 \\\\C_2 = 118.58 \ in[/tex]

After one rotation, the larger tire will travel the following distance more than  the smaller tire;

[tex]n = \frac{C_2}{C_1} = \frac{118.58}{104.94} = 1.13[/tex]

The distance Janessa traveled on the new tires when her odometer shows she has traveled 23425 miles;

[tex]distance = 1.13 \times 23,425\\\\distance = 26,470.25 \ miles[/tex]

Learn more about tire sizes and distance traveled: https://brainly.com/question/4822144

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.