2004 AMC 10A Problem 17

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:

Starting from opposite points, together they cover half the track before their first meeting

Big hint:

Use the constant speed ratio to compare Brenda’s first-meeting distance with her distance between meetings

Solution:

Before the first meeting the two together cover half the track. Between the first and second meetings they together cover a full track, which is twice as far, so Brenda runs

2 \cdot 100 = 200

meters in that stretch.

Sally runs

150

meters in the same stretch, so the full track length is

200 + 150 = 350.

Thus, the correct answer is C.