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 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

Answer 1

Answer:

  C.  2.0 < t < 2.5

Step-by-step explanation:

  time = distance / speed

The circumference of the lake is given by ...

  C = πd = 2π miles ≈ 6.28 miles

Then Johanna's time is ...

  (6.28 mi)/(3 mi/h) ≈ 2.09 h

This time is in the interval (2, 2.5), so matches choice C.

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Alternate solution

If we take pi to be 3, then this boils down to ...

  2×3/3 = 2 . . . hours

Pi is on the order of 5% more than 3, so her time will be on the order of 5% more than 2 hours, or just above 2, but not as great as 2.5 hours. This sort of estimating can get you to the correct answer without a calculator.