A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around...

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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 speed 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

OA C

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GMAT Prep

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 speed 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

OA C
Solution:

If the lake has a diameter of 2 miles, its radius is 1 mile, and its circumference (which is the length of the track) is 2 x π x 1 = 2π miles long. Since Johanna’s speed is 3 miles per hour, then the time it took her to walk around the lake is 2π/3 hours. Since π ≈ 3.14, then 2π/3 ≈ 6.28/3 ≈ 6.3/3 = 2.1 hours.

Answer: C

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