Question

Three athletes start together to travel the same way
around on a circular path of 12 km with speeds of 3
km/ph, 4 km/ph and 6 km/ph respectively. They meet at
the same point again after what time?
(a) 12 h (6)8 h . (c) 16 h (d)10 h​

Answer 1

Answer:

Each must travel an integral number of laps

S = V * T = N * 12    where N is the number of laps traveled

T = N1 * 12 / 3 = N2 * 12 / 4 = N3 * 12 / 6   since they all travel for the same time

N1 / 3 = N2 / 4 = N3 / 6

Multiply by 12 and

4 N1 = 3 N2 = 2 N3 = T

T = 12 hrs     N1 = 3 laps, N2 = 4 laps  and N3 = 6 laps

12 is the smallest number divisible by 3, 4, 6

Or more simply at 3 km/hr it takes 4 hrs and at 4 km/hr it takes 3 hrs and

at 6 km/hr it takes 2 hrs to get back to the same point, so what is the smallest number divisible by 3, 4, 6