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a car's wheels are 28 in. in diameter. how far (in miles) will the car travel if its wheels revolve 10,000 times without slipping?

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2 Answers

If the wheels turn 10,000 times, the car will travel 10,000 times the circumference of the wheel. This is because it does not slip- you can see how this affects the movement just by rolling around anything round.

The circumference of a circle is pi*diameter, which in this case is pi*28" = 87.9646 inches. Multiplying by 10,000, we get 879,646 inches. Now we just have to convert to miles. 

879,646 inches *(1 foot/12 inches)= 73,303.83 feet

73,303 feet* (1 mile/5280 feet)= 13.88 miles

The distance traveled, denoted by S, is the total number of wheels revolutions (10,000) times the circonference of the wheel (pi. D = pi x 28") = 10,000 x pi x 28" .To convert this distance in miles, remember that there are 1760 yards in a mile, 3 feet in a yard and 12" in a foot.Thus to find  the total distance in miles you have to divide the total distance in inches by how many inches in a mile.

Thus, S = 10,000 x pi x 28 / (1760 x 3 x 12) = 13.88 miles