3 swimmers start swimming laps at the same time in a 25yd pool. At what point will they all cross paths at the same time?

Question

Let swimmer 1 rate = 50yds/min

swimmer 2 rate = 40yds/min

swimmer 3 rate= 30yds/min

Answer 1

The swimmers are swimming laps and thus the number of laps does not matter but the remainder of feet into the next lap does. The number of pool lengths must be even though for the swimmers to be the same distance from the same side. To have them all at one end we must find a time when all swimmers have swum a distance divisible by 50. All rates are divisible by 10. Thus at 5 minutes all distances will be divisible by 50. At 5 minutes the first swimmer has swum 250 feet or 10 lengths, the second 200 feet or 8 lengths and the last has swum 150 feet or 6 lengths.

Answer 2

Every 200 yards or every 8 laps swimmer 1 and 2 will cross.

Swimmer 3 crosses swimmer 2 every 120 yards, and crosses swimmer 1 every 150 yards

Every 600 yards, they all cross at the same time, or every 24th lap, assuming they really keep up a constant speed by then.

You're looking for the least common multiple of 30, 40 and 50. 600 is the smallest number divisible evenly by all three speeds. 10 is a common factor 3x4x5=60 is the least common multiple of these factors. 60x10=600