A and B were joging along a circular track. Track is 640m, if they start from same place & jogged in same direction A would take 16min to catchup B.

Question

A and B were joging along a circular track. Track is 640m, if they start from same place & jogged in same direction A would take 16min to catchup B. If they jogged in oppo direction, they would meet every 4 min. How long would A take to jog 1 round?

Answer 1

Let a and b denote the speeds of A and B respectively. Let the length of the circular track be T. Since A would take 16min to catch up to B if they jogged in the same direction, this implies that A makes one more lap than B. So we know that A is faster than B, and a > b. We can then deduce that (a - b)*16 = T.

If A and B jogged in the opposite directions, they would take 4 mins to complete the same distance of T. So we have that (a + b)*4 = T. Putting these equations together and solving for a, we get that 12a = 20b, and a = (5/3)b. (or b = 3/5*a)

Let x be the time taken for A to jog 1 round. Since A must run the distance T on her own, we can set up the following equation: (a + b)*4 = xa = T. Subbing in the expression for b we found earlier, we have (a + 3/5 a)*4 = xa. Solving for x, we have that x = 32/5. Hence it takes A 6 and 2/5 mins to job 1 round on her own.

Note that we do not need to know the length of the circular track to solve this problem.