Continuing with the original problem. Three friends A B & C regularly jog in circular jogging track every morning. The track is 1000 m in circumference.

A takes 8 mins to complete one lap, B takes 10 mins & 40 secs & C takes 12 mins. They all start from a point on the track but C decides to run in the opposite direction from the same point.

As they set out B suddenly has cramps (not at the starting point) and starts walking in the same direction as before. His walking speed takes him 32 mins to complete a lap. He decides to continue walking till they all meet. At what point should he have cramps such that they all meet at any point in the fastest time?

A can take 8 mins to jog the track (1 lap) so it means A has the speed of 125meters per munite in a 1000meters track. B can take 10.66667 munites the whole track which is 93.75 meters per munite and lastly C can take it for 12 munites which is 83.33 meters per munite.. but C is in the opposite direction,,,since A is faster than B...... so  C will meet first A because he is faster than B.  Assume that the direction of A and B is starting at 0 to 1000m. C and A will meet at.......

compare the percentage of A and C. 

125m + 83.33m = 208.33m

 for A:      125m / 208.33m = .60000

                  .60000 (100%) = 60%

for B:       100% - 60% = 40%

60% of the 1000m track is  = 600m. So A and C will meet at 600m

C and B will meet at:

compare the percentage of C and B

83.33m + 93.75m = 177.08m

for B: 93.75m / 177.08m = .52941

          .52941 (100%) = 52.941%

for C: 100% - 52.941% = 47.059%

52.941% of 1000m track is = 529.41m

@ 529.41m. C started to cramps

NOTE: there is no way that the three will meet at any point in a track

 

Posted by manuel on 2006-07-26 10:36:06