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?

$250$

$300$

$350$

$400$

$500$

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.

2004 AMC 12A Problem 15

Solution:

Problem 15 in Other Years