2004 AMC 12A Problem 15

Question

Brenda and Sally run in opposite directions on a circular track, starting at diametrically opposite points. They first meet after Brenda has run

100

meters. They next meet after Sally has run

150

meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

250

300

350

400

500

Answer: C

Concepts:relative speed distance rate and time ratio and proportion

Difficulty rating: 1540

Small hint:

By the first meeting the two together have covered half the track

Big hint:

Between the first and second meetings they together cover a full track, so Brenda runs twice her first leg

Solution:

Starting at opposite ends, when they first meet they have together run half the track. Between the first and second meetings, they together run a full track length.

Since Brenda runs at a constant speed and covered

100

meters before the first meeting, she covers

2 \cdot 100 = 200

meters between the two meetings.

Adding Sally’s

150

meters over that same interval gives a track length of

200 + 150 = 350

meters.

Thus, the correct answer is C.