1959 AMC 12 Problem 30

Attempt Problem 30 of the 1959 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 1959 AMC 12 solutions, or check the answer key.

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

30.

AA can run around a circular track in 4040 seconds. B,B, running in the opposite direction, meets AA every 1515 seconds. What is BB’s time to run around the track, expressed in seconds?
121212\dfrac12
2424
2525
271227\dfrac12
5555
Answer: B
Concepts:relative speedrate
Small hint:
Measure each runner’s speed in laps per second
Big hint:
Because they run in opposite directions, their speeds add to 115\frac{1}{15} lap per second
Solution:
If BB’s lap time is t,t, their relative speed is 140+1t=115. \frac1{40}+\frac1t=\frac1{15}. Thus 1t=124,\frac{1}{t}=\frac{1}{24}, so t=24t=24 seconds.
Therefore, the correct answer is B.
LIVE by Po-Shen Loh
Programs

LIVE Classes

Self-Paced Classes

Stars

Scholarship

About Us

Who Is Po-Shen Loh?

Email Contact

Newsletter

Jobs

Become a Star

For a more Thought Full world.

© 2026 Expii, Inc.