When two runners will meet

[daboa]

Hi! I had this problem on a test today.

A is running 3 laps on 10min. B is running 5 laps on 12 min. After how many laps, done by A and B together, will they meet at the startline at the same time?

I think my answer was 18 laps and, I dont remember the other one. I'm not sure that it's correct. I would like to see a proof. How would you solve it? Thank you

[amirhtlusa]

i have seen this problem before, it's an easy problem.

[amirhtlusa]

your answer for A was correct! A=18, B=25
here is the proof:
in each minute, A runs .3 laps and B runs 5/12 laps.
so we know that B runs faster. therefore it takes 12/5 mins for B to run one lap. so when B runs one lap, then A has ran:
(.3)*(12/5)=36/50
now, you can say that if B completes X laps, then A will complete 36X/50 laps, now all you need to do is to find the smallest value of X. which is 25.
so B will complete 25 laps, and A will complete 18. and they will meet in the same time.