Question

lucy races her bicycle for 258 ft. a wheel of her bicycle turns 43 times as the bicycle travels this distance. what is the diameter of the wheel? use the value 3.14 for π. round your answer to the nearest tenth. do not round any intermediate steps.

Explanation:

Step1: Find the circumference of the wheel

The total distance traveled is 258 ft and the wheel turns 43 times. The circumference \(C\) of the wheel is the total - distance divided by the number of turns. So \(C=\frac{258}{43}\) ft.
\[C = 6\text{ ft}\]

Step2: Use the formula for the circumference of a circle

The formula for the circumference of a circle is \(C=\pi d\), where \(d\) is the diameter. We know \(C = 6\) ft and \(\pi=3.14\). Rearranging the formula for \(d\), we get \(d=\frac{C}{\pi}\).
\[d=\frac{6}{3.14}\text{ ft}\]
\[d\approx1.9\text{ ft}\]

Answer:

1.9 ft