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

Explanation:

Since, the diameter of the lake = 2 miles,

⇒ Radius of the lake =
`(Diameter)/(2)` = 1 mile,

Circumference of the lake =
`2\pi* radius`

`=2\pi\text{ miles}`

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

Speed = 3 miles per hour,

We know that,

`Speed =(Distance)/(Time)`

`\implies Time =(Distance)/(Speed)`

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

`t=(2\pi )/(3)\approx 2.094\text{ hours}`

∵ 2.0 < 2.094 < 2.5

Hence, OPTION c. is correct.