How long until they they are together again at the start/finish line?

Question

Jan and Tyrell are running laps for exercise on a circular track. Tyrell takes five minutes (or 300 seconds) to complete a lap around the track. Jan takes 2 and a half minutes (or 150 seconds). If they are both together now at the start/finish line, how long will it be until they are together again at the start/finish line?

Answer 1

In the first 150 seconds Jan has made one lap, and Tyrell is only half way through.

Let's start from there and consider this a RTD problem

Tyrell's rate is 0.2 lpm (lap per minute). He has a 0.5 lap "lead."

Jan's rate is 0.4 lpm

0.4t = 0.2t + 0.5

0.2t = 0.5

t = 2.5

This is added to the first 2.5 minutes.

 

Now that is the math - rather cumbersome!

When Tyrell is half way, Jan has run one lap and is catching up

When Tyrell does the second half, Jan has run another lap and meets Tryrell at the starting point.

It takes Jan 5 minutes to run two laps and Tyrell 5 minutes to run one lap.