Three friends A, B and C regularly jog in a
circular jogging track every morning. The track is 1000 m in circumference.
A takes 8 mins to complete one lap, B takes 10 mins and 40 secs and C takes 12 mins. All of them setout from a same point but C runs in the opposite direction from starting point.
Another friend D joins this run. D normally takes 13 mins and 20 secs to complete one lap. He decides to run in the same direction as C but from a point 600 m ahead of C in his jogging direction. When will they all meet each other on the circular track & where?
(In reply to
Puzzle Answer by K Sengupta)
A and B takes 8 min and 32/3 min respectively to complete one lap.
=> A and B will meet at the starting point after lcm(8, 32/3) = 32 min
C completes 1 lap in 12 minutes.
So he will meet both A and B for the first time in lcm(12,32)= 96 minutes.
Now, D starts 400 m from the starting point.
He takes 40/3 minutes to complete one lap (1000 m), so he will traverse 400 m in 16/3 minutes, and he will have done 2 more complete laps after a total of 32 minutes.
Thus, we need to solve for 32 + (40/3)*x = 96*y.
We observe that the minimum value of y =1 do not yield any solution.
y=2 gives x=12.
Consequently, A, B, C, and D will meet for the first time in 192 minutes at the starting point.
Edited on May 23, 2022, 10:39 pm
Explanation to Puzzle Answer
