SOLUTION: two athelets P and Q are running around a circular track of 1200m at speeds of 6mps and 3mps respectively.Both of them start from the same point in the same direction but P revers

Question 765630: two athelets P and Q are running around a circular track of 1200m at speeds of 6mps and 3mps respectively.Both of them start from the same point in the same direction but P reverses his direction every time he completes one round.After how much time from the start will they meet for the first time?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
as far as i can tell, they will meet at the 800 meter mark.
they both start at the 0 meter mark.
p is going at 6 meters per second and q is going at 3 meters per second.
p will be at the 1200 meter mark in 200 seconds.
q will be at the 600 meter mark in 200 second.
p reverses his direction.
they are now 600 meters apart.
since they are running towards each other their rates will be additive.
the formula is rate * time = distance.
the distance is 600 meters.
the formula becomes:
(r1 + r2) * time = distance
this formula becomes:
(6m/s + 3m/s) * time = 600m
simplify to get:
9m/s * time = 600m
divide both sides by 9m/s to get:
time = 600m / (9m/s) which becomes:
time = 600m * (s/9m) which then simplifies to:
time = 66.6666667 seconds
the total distance traveled is 600 meters in 66.6666667 seconds.
p will have traveled 66.6666667 * 6 = 400 meters in 66.6666667 seconds.
q will have traveled 66.6666667 * 3e = 200 meters in 66.666667 seconds.
p is going backwards from the 1200 meter mark to the 800 meter mark.
p is going forward from the 600 meter mark to the 800 meter mark.
they will meet at the 800 meter mark.
total time traveled is 200 + 66.6666667 seconds.
in 200 seconds, p has gone forward from the 0 meter mark to the 1200 meter mark.
in another 66.6666667 seconds, p has gone backwards from the 1200 meter mark to the 800 meter mark.
in 200 seconds, q has gone forward from the 0 meter mark to the 600 meter mark.
in another 66.6666667 seconds, q has continued to go forward from the 600 meter mark to the 800 meter mark.

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