1995 AMC 12 Problem 7

Attempt Problem 7 of the 1995 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1995 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The radius of Earth at the equator is approximately

4000

miles. Suppose a jet flies once around Earth at a speed of

500

miles per hour relative to Earth. If the flight path is a negligible height above the equator, then, among the following choices, the best estimate of the number of hours of flight is

8

25

50

75

100

Answer: C

Concepts:circumference rate

Difficulty rating: 1220

Small hint:

Approximate the equator’s length with

2\pi r

Big hint:

Divide the trip distance by

500

and use a simple estimate for

\pi

Solution:

The equator is approximately

2\pi(4000)=8000\pi

miles long. The flight time is

\frac{8000\pi}{500}=16\pi\approx50

hours. Thus the correct answer is C.