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 avera

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

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Katherine 2 weeks 2021-09-13T12:57:20+00:00 1 Answer 0

Answers ( )

  1. Answer:

    c. 2.0 < t < 2.5

    Step-by-step explanation:

    Since, the diameter of the lake = 2 miles,

    ⇒ Radius of the lake = \frac{Diameter}{2} = 1 mile,

    Circumference of the lake = 2\pi\times radius

    =2\pi\text{ miles}

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

    Speed = 3 miles per hour,

    We know that,

    Speed =\frac{Distance}{Time}

    \implies Time =\frac{Distance}{Speed}

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

    t=\frac{2\pi }{3}\approx 2.094\text{ hours}

    ∵ 2.0 < 2.094 < 2.5

    Hence, OPTION c. is correct.

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