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?
Q. 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?
Calculate Circumference: Calculate the circumference of Nathan's bike tire. The formula for the circumference of a circle is C=2⋅π⋅r, where r is the radius. Nathan's bike tire radius = 1 foot. Circumference of Nathan's bike tire = 2⋅π⋅1=2π feet.
Calculate Distance Traveled: Calculate the distance Nathan's bike travels after 15 revolutions.Distance = Circumference × Number of revolutions.Distance traveled by Nathan's bike =2π×15.Distance traveled by Nathan's bike =30π feet.
Calculate Circumference: Calculate the circumference of Reed's bike tire.Reed's bike tire radius = 2 feet.Circumference of Reed's bike tire = 2×π×2=4π feet.
Calculate Distance Traveled: Calculate the distance Reed's bike travels after 15 revolutions.Distance traveled by Reed's bike = 4π×15.Distance traveled by Reed's bike = 60π feet.
Calculate Difference: Calculate the difference in distance traveled between Reed's and Nathan's bikes.Difference in distance = Distance traveled by Reed's bike - Distance traveled by Nathan's bike.Difference in distance = 60π−30π.Difference in distance = 30π feet.
Convert and Round: Convert the difference in distance to a numerical value and round to the nearest tenth. π is approximately 3.14159.Difference in distance ≈30×3.14159.Difference in distance ≈94.2477 feet.Rounded to the nearest tenth, the difference is approximately 94.2 feet.
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