After what minimum time they meet first at B, will they again meet at B?

Question

Two men start a bicycle race at triangular track ABC.

Starting from the point A simultaneously, one of them traverse the track in clockwise sense A-> B -> C & the other in anticlockwise sense A-> C-> B with their respective constant speed. After 4 min from the start, they first meet at B and then continue the race.

After what minimum time they meet first at B, will they again meet at B? Distance AB=500m, BC=400m, CA=300m

Answer 1

Answer: 48 minutes

speeed1 x 4minutes = 500m and speed2 x 4 minutes = 700m ---> speed2 = 1.4 x speed1
speed1 = 500m per 4minute = 125m per minute and speed2 = 175m per minute
track length BCAB or BACB = 400+300+500=1200m
both will meet at point B when both make a full lap (from point B) at the same time ---> speed1 on 5th lap and speed2 on 1.4 x 5 laps = 7th lap
so for speed1 total travels = 5 x 1200m = 6000m ----> time = 6000/125 = 48 minutes
speed2 total travels = 7 x 1200m = 8400m ----> time = 8400/175 = 48 minutes (checked)