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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

Step-by-step explanation:

Since, the diameter of the lake = 2 miles,

⇒ Radius of the lake = [tex]\frac{Diameter}{2}[/tex] = 1 mile,

Circumference of the lake = [tex]2\pi\times radius[/tex]

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

Total distance he/she has to cover = [tex]2\pi[/tex] miles

Speed = 3 miles per hour,

We know that,

[tex]Speed =\frac{Distance}{Time}[/tex]

[tex]\implies Time =\frac{Distance}{Speed}[/tex]

Thus, the time taken by her/him ( say t ),

[tex]t=\frac{2\pi }{3}\approx 2.094\text{ hours}[/tex]

∵ 2.0 < 2.094 < 2.5

Hence, OPTION c. is correct.

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