Problema Solution

reinette and chienny run at constant speed along a circular track 1350 meters in circumference. running in opposite directions, they meet every 3 minutes, while running in the same direction they are together every 27 minutes. find their speed

Answer provided by our tutors

distance = speed * time


we are going to assume that Reinette is the faster runner since the problem does not provide enough information to know which runner is faster; the problem also does not specify what units their speed should be expressed in, so we choose meters per second (m/s)


let 'r' represent Reinette's speed in m/s and 'c' represent Chienny's speed in m/s, the running in opposite directions their relative speed is represented by 'r+c' and running in the same direction their relative speed is represented by 'r-c'


since we are calculating speed as meters per second, we convert our times to seconds:

3 minutes = 180 seconds

27 minutes = 1620 seconds


we have these two distance formulas:

1350 = (r+c)180

1350 = (r-c)1620

solving this system we have:

c = 3 1/3

r = 4 1/6


so since we assumed Reinette is the faster runner, Reinette's speed is 4 1/6 m/s, Chienny's speed is 3 1/3 m/s