2011 AMC 12B Problem 8

Problem 8 of 25EasierAlgebra Geometry

Keiko walks once around a track at exactly the same constant speed every day. The sides of the track are straight, and the ends are semicircles. The track has width

6

meters, and it takes her

36

seconds longer to walk around the outside edge of the track than around the inside edge. What is Keiko’s speed in meters per second?

Show solution

Solution

The straight sides are the same length for both paths, so the difference in length comes only from the two semicircular ends. If the inner radius is

r,

those ends combine into a full circle, and the extra length is

2\pi(r+6)-2\pi r=12\pi.

If her speed is

x

meters per second, then the extra time gives

36x=12\pi,

x=\dfrac{\pi}{3}.

Thus, the correct answer is A.

Answer choices

Solution

More practice