Mits83 Posted July 18, 2006 Share Posted July 18, 2006 P,Q and S are running a race on a circular track of circumference of 2100 m. When P completes one round, Q is 700m behind him. When S completes one round, Q is 300m ahead of him. What is the minimum distance from the starting point when they are together again? A) 300m B) 700m C) 2100m D) 16800m E) None of these Quote Link to comment Share on other sites More sharing options...
rufus16 Posted July 18, 2006 Share Posted July 18, 2006 The meeting point of Q and S for the first time is at 16800 m .(LCM of 2100 and 2400) . P naturally wwould be there, as it is also the LCM of 16800 and 2100 . So the answer should be 16800 . Quote Link to comment Share on other sites More sharing options...
mishu007 Posted July 18, 2006 Share Posted July 18, 2006 i cant understand ur procedure... could you plz show me the details...... Quote Link to comment Share on other sites More sharing options...
Mits83 Posted July 19, 2006 Author Share Posted July 19, 2006 right, rufus. Answer is 16800. Quote Link to comment Share on other sites More sharing options...
mishu007 Posted July 19, 2006 Share Posted July 19, 2006 right, rufus. Answer is 16800. But i cant understood the process... plz help me........ Quote Link to comment Share on other sites More sharing options...
arjmen Posted July 19, 2006 Share Posted July 19, 2006 P,Q and S are running a race on a circular track of circumference of 2100 m. When P completes one round, Q is 700m behind him. When S completes one round, Q is 300m ahead of him. What is the minimum distance from the starting point when they are together again? A) 300m B) 700m C) 2100m D) 16800m E) None of these The question is not worded correctly. P, Q and S are running at different speeds. When they meet again, they'd have run different distances. Assuming the runners speeds are constant, for every 2100m that S runs, Q will run 2400 and P will run 2400*(2100/1400) = 3600m When the runners next meet, Q has to have run a multiple of 2100m more than S and P has to have run a multiple of 2100m more than Q (and a higher multiple of 2100m more than S). Q will lap S once every 7 [= 2100/(2400-2100)] laps P will lap S once every 1.4 [= 2100/(3600-2100)] laps So they'd all meet again for the first time when P, Q and S have completed 12, 8 and 7 laps respectively. Distance run by P = 12*2100 = 25,200m Distance run by Q = 8*2100 = 16,800m Distance run by S = 7*2100 = 14,700m Quote Link to comment Share on other sites More sharing options...
Mits83 Posted July 19, 2006 Author Share Posted July 19, 2006 Arjmen, can u assume that the speeds are constant? I don't think so.. Quote Link to comment Share on other sites More sharing options...
Mystery Man Posted July 19, 2006 Share Posted July 19, 2006 Well if we are calculating on the basis of 2100 we'll get the next time they meet at the start. Having different speeds can they not meet somewhere in the middle of the track? Quote Link to comment Share on other sites More sharing options...
coolgeek Posted July 19, 2006 Share Posted July 19, 2006 rufus is correct if any body dont understand use the following steps consider P and Q when P runs 2100 m Q runs only 1400 m take Q and S when Q runs 2400 m S runs 2100 m this is 3:2 and 8:7 ratio which means 12:8:7 is the combined ratio that is P runs 1200m Q runs 800m and S runs 700m in the same time find the LCM of 12 8 and 7 u will get 168 so D shuld be the ans Quote Link to comment Share on other sites More sharing options...
Mystery Man Posted July 19, 2006 Share Posted July 19, 2006 Got the point. Quote Link to comment Share on other sites More sharing options...
arjmen Posted July 19, 2006 Share Posted July 19, 2006 Arjmen, can u assume that the speeds are constant? I don't think so.. I'd love to know how you'd solve this question without assuming that the runners run at their respective constant speeds (or atleast that their respective average speeds are constant). The answer to the question as is cannot be 16,800m because that is the minimum distance run by Q before the three runners meet. P would have run a longer distance and S a shorter distance than Q. The only way the runners can meet if they're running at different speeds round a track is if the fastest runner laps the second fastest and the slowest at the same instant. The three must therefore have run different distances (the difference in the distances run have to be multiples of 2100m (the length of the track). Had the question asked "What is the distance run by Q before the three runners meet for the first time after starting?", then the answer would be 16,800m. But that is not what the question asks. Well if we are calculating on the basis of 2100 we'll get the next time they meet at the start. Having different speeds can they not meet somewhere in the middle of the track? In this question the speeds are such that the 3 will meet only at the start line everytime they meet. Quote Link to comment Share on other sites More sharing options...
arjmen Posted July 19, 2006 Share Posted July 19, 2006 Repeated post. Quote Link to comment Share on other sites More sharing options...
bohemian Posted July 21, 2006 Share Posted July 21, 2006 P,Q and S are running a race on a circular track of circumference of 2100 m. When P completes one round, Q is 700m behind him. When S completes one round, Q is 300m ahead of him. What is the minimum distance from the starting point when they are together again? A) 300m B) 700m C) 2100m D) 16800m E) None of these I think ..it must be 0 ..the minimum distance from the starting point when they meet again. As they always meet in the starting point. Hence my choice go for E Quote Link to comment Share on other sites More sharing options...
eddycurrent Posted July 24, 2006 Share Posted July 24, 2006 yeah if the question is EXACTLY worded as it is...i think 0 is the answer too.... hi just out of curiosity...where did you get this question from??:) Quote Link to comment Share on other sites More sharing options...
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