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Nathan and Reed are racing their dirt bikes. Nathan's bike tire has a radius of 1 foot, and Reed's bike tire has a radius of 2 feet. If both tires rotate 15 revolutions, how many feet further does Reed's bike travel, rounded to the nearest tenth?

Nathan and Reed are racing their dirt bikes. Nathan's bike tire has a radius of 11 foot, and Reed's bike tire has a radius of 22 feet. If both tires rotate 1515 revolutions, how many feet further does Reed's bike travel, rounded to the nearest tenth?

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Q. Nathan and Reed are racing their dirt bikes. Nathan's bike tire has a radius of 11 foot, and Reed's bike tire has a radius of 22 feet. If both tires rotate 1515 revolutions, how many feet further does Reed's bike travel, rounded to the nearest tenth?
  1. Calculate Circumference: Calculate the circumference of Nathan's bike tire. The formula for the circumference of a circle is C=2⋅π⋅rC = 2 \cdot \pi \cdot r, where rr is the radius. Nathan's bike tire radius = 11 foot. Circumference of Nathan's bike tire = 2⋅π⋅1=2π2 \cdot \pi \cdot 1 = 2\pi feet.
  2. Calculate Distance Traveled: Calculate the distance Nathan's bike travels after 1515 revolutions.\newlineDistance == Circumference ×\times Number of revolutions.\newlineDistance traveled by Nathan's bike =2π×15= 2\pi \times 15.\newlineDistance traveled by Nathan's bike =30π= 30\pi feet.
  3. Calculate Circumference: Calculate the circumference of Reed's bike tire.\newlineReed's bike tire radius = 22 feet.\newlineCircumference of Reed's bike tire = 2×π×2=4π2 \times \pi \times 2 = 4\pi feet.
  4. Calculate Distance Traveled: Calculate the distance Reed's bike travels after 1515 revolutions.\newlineDistance traveled by Reed's bike = 4π×154\pi \times 15.\newlineDistance traveled by Reed's bike = 60π60\pi feet.
  5. Calculate Difference: Calculate the difference in distance traveled between Reed's and Nathan's bikes.\newlineDifference in distance = Distance traveled by Reed's bike - Distance traveled by Nathan's bike.\newlineDifference in distance = 60π−30π60\pi - 30\pi.\newlineDifference in distance = 30π30\pi feet.
  6. Convert and Round: Convert the difference in distance to a numerical value and round to the nearest tenth. \newlineπ\pi is approximately 3.141593.14159.\newlineDifference in distance ≈30×3.14159\approx 30 \times 3.14159.\newlineDifference in distance ≈94.2477\approx 94.2477 feet.\newlineRounded to the nearest tenth, the difference is approximately 94.294.2 feet.

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