Question

A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average rate of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?A. 0.5< t < 0.75

B. 1.75< t < 2.0
C. 2.0 < t < 2.5
D. 2.5 < t < 3.0
E. 3 < t < 3.5

Answer 1

C. 2.0 < t < 2.5

`t = 2.094 \text{hours}`

Explanation:

Johanna's avg speed is given in mph = 3mph.

The circumference of the circular track is the length(D) of one revolution of the track.

`D=2\pi r = 2 \pi (1)`

`D=2\pi\,\text{miles}`

now, since we have the average speed of Johanna. we can use:

`\text{speed}=\frac{\text{distance}}{\text{time}}`

and solve for time

`3 \frac{\text{mile}}{\text{hour}}= \frac{2\pi\,\text{mile}}{t\,\text{hour}}`

`t = (2\pi)/(3)`

`t = 2.094 \text{hours}`

the time time it took for Johanna is more than 2 hours. Option C is correct.