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