Final answer:
To find the bicycle's speed in mph, calculate the tire circumference and multiply by revolutions per minute. Convert the result from inches per minute to miles per hour to get the final speed: 15.46 mph.
Step-by-step explanation:
To calculate how fast the bicycle is traveling, we need to determine the distance covered per minute and then convert that to miles per hour. First, we calculate the circumference of the bicycle's tire using the formula C = 2πr, where r is the radius of the tire. With a radius of 13 inches, the circumference C is 2π(13 inches). Next, we find the distance traveled in one minute by multiplying the number of revolutions per minute by the circumference. As the bicycle makes 200 revolutions per minute, the total distance covered in one minute is 200 revolutions × C. Now we convert inches to miles and minutes to hours to obtain the speed in miles per hour (mph).
To calculate how fast the bicycle is traveling in miles per hour, we can use the formula:
Speed = Circumference x Revolutions per minuteFirst, let's calculate the circumference of the tires. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. Therefore, the circumference of the bicycle tires is C = 2 x π x 13 inches.Next, we need to convert inches to miles. Since there are 12 inches in a foot and 5280 feet in a mile, the conversion factor is 1 mile/63360 inches.Now, let's calculate the speed:Speed (miles per hour) = (Circumference x Revolutions per minute) x (1 mile/63360 inches) x (60 minutes/1 hour)To put this into practice:Calculate the circumference: C = 2π(13 inches) ≈ 81.68 inches.Multiply by revolutions per minute: 81.68 inches/revolution × 200 revolutions/minute ≈ 16,336 inches/minute.Convert inches to miles (÷ by 63,360 inches/mile): 16,336 inches/minute / 63,360 inches/mile ≈ 0.2577 miles/minute.Finally, convert minutes to hours (× by 60 minutes/hour): 0.2577 miles/minute × 60 minutes/hour ≈ 15.46 mph.Thus, the bicycle is traveling at 15.46 mph.