Question

Two particles move at different but constant speeds along a circle of circumference 276 ft. Starting at the same instant and from the same place, when they move in opposite directions, they pass each other every 6 seconds and when they move in the same direction they pass each other every 23 seconds. Determine their rates.

Answer 1

This is the concept of relative speed, given that the particles are moving at a circumference of 276 ft and they have the speed x and y, this rate can be calculated as follows;
Relative speed of the particles are moving towards each other will be:
(x+y) ft/s
time taken for them to meet will be:
time=distance/speed
time=276/(x+y)=6
thus;
276=6x+6y
this can be simplified as
46=x+y....i
Time taken for them to meet when they are moving away from each other will be:
relative speed=x-y
thus;
time=276/(x-y)=23
this can be written as:
276=23x-23y
when we simplify we get
12=x-y.....ii
from ii,
x=12+y....iii
substituting iii in i we get
46=x+y
46=12+y+y
46-12=2y
34=2y
y=17
x=12+y
x=12+17
x=29
therefore we conclude that particle A is moving at 29 ft/s and B at 17 ft/s