- Three friends A, B and C run around a circular track of length 120
metres at speeds of 5 m/s, 7 m/sec and 15 m/sec, starting simultaneously
from the same point and in the same direction. How often will the three of
them meet?
(1) Every 60 seconds (2) Every 120 seconds (3) Every 30 seconds (4) None of these
Solution:
The problem can be solved as follows:
First find out when A and B will meet for the first time.
A and B will meet for the first time in (Circumference of track / relative speed) seconds = (120/2) = 60 seconds.
This also means that A and B will continue meeting each other every 60 seconds.
Next find out when B and C will meet for the first time.
B and C will meet for the first time in (120/8) = 15 seconds.
This also means that they will meet every 15 seconds after they meet for the first time.
i.e. A and B meet every 60 seconds and multiples of 60 seconds and B and C meet every 15 seconds and multiples of 15 seconds.
The common multiples to both these time, will be when A and B and B and C will meet � i.e when A, B and C will meet.
The common multiple of 60 and 15 will be 60, 120, 180 etc.
i.e. they will meet every 60 seconds.
