Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

prealgebra intermediate

Problem

Two bicycle racers cross the starting line on a circular track at 12:15 PM. One cyclist takes minutes per lap, while the other completes a lap every minutes. Assuming their speeds remain constant, what is the next time they cross the starting line together? Your answer should be in the form like 3:45.
Solution
We seek the least common multiple of minutes and minutes. This gives the amount of time that transpires until the two again cross the starting line together. and , so taking the highest power of each yields minutes, so that the desired time is minutes past , or .
Final answer
\text{1:03 PM}