SOLUTION: In a circular track of 63 meters two runners run with speeds 9m/s and 7 m/s. At how many distinct meeting points will they meet? i figured they meet every 31.5 second and i work

Question 984311: In a circular track of 63 meters two runners run with speeds 9m/s and 7 m/s. At how many distinct meeting points will they meet?
i figured they meet every 31.5 second and i worked out that the number of distinct meeting points is 2. however, what i do not understand is this solution that you can take the ratio of the speeds in simplest form, subtract, and then get the number of distinct meeting points.
What I mean is 9-7 =2 which is your answer
Can you please derive this method.
I AM LITERALLY LOOSING it, i cannot understand how this works even though it is correct.
please help me i've been asking since yesterday.
Also if they were traveling in opposite directions the method says to add 9 and 7 which gives you 16 distinct meeting points. I don't understand this either.
I AM LITERALLY LOOSING it, I cannot understand how this works even though it is correct.
please help me i've been asking since yesterday!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
circular track of 63 meters two runners run with speeds 9m/s and 7 m/s,
use rate * time = distance
a) the faster runner will complete the track in 7 seconds and the slower runner will complete the track in 9 seconds, therefore they will only meet at the beginning and the end which is 2 points.
b) running in opposite directions, the faster runner will overlap the slower runner at 63 - 49 + 2 = 16 points
note that the 2 is for the beginning and end

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