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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

Respuesta :

Answer:

C. 2.0 < t < 2.5

[tex]t = 2.094 \text{hours}[/tex]

Step-by-step 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.

[tex]D=2\pi r = 2 \pi (1)[/tex]

[tex]D=2\pi\,\text{miles}[/tex]

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

[tex]\text{speed}=\dfrac{\text{distance}}{\text{time}}[/tex]

and solve for time

[tex]3 \frac{\text{mile}}{\text{hour}}= \dfrac{2\pi\,\text{mile}}{t\,\text{hour}}[/tex]

[tex]t = \dfrac{2\pi}{3}[/tex]

[tex]t = 2.094 \text{hours}[/tex]

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

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