SOLUTION: Two objects are moving uniformly with different speeds in a circular track whose length is 280 m. If they move in the saem direction, they will meet oonce in every 56 minutes. If t

Question 761349: Two objects are moving uniformly with different speeds in a circular track whose length is 280 m. If they move in the saem direction, they will meet oonce in every 56 minutes. If they move in opposite directions, they will meet once in every 8 mins. Find the speed of the objects.
PLEASE HELP ME!!!!
thanks
Answer by ramkikk66(644) (Show Source): You can put this solution on YOUR website!

Let the objects be obj1 and obj2. Let x and y be their speeds. Assume that they start from the same point in the track, and that y is the faster of the 2.
1) When they are travelling in opposite directions, in 8 min, obj1 will travel 8*x m, and obj2 will will travel 8*y m. But since they meet after 8 min, it means that the total distance covered by them must be equal to the length of the track.
So,

or
----> eqn 1

2) When they are travelling in the same direction, and meet again, it means that the faster object has run one extra time around the track. From the moment they start, the faster object is always ahead of the slower object. So the only time they can meet is when the faster completes the track and then "catches up" with the slower object.

So, in 56 min, distance run by the faster object obj2 = distance run by the slower object obj1 + the length of the track.

or ----> eqn 2 (dividing both sides by 56)

Substituting for y as x+5 from eqn 2 into eqn 1
or

Speed of slower object = 15 meters/min
Speed of faster object = 20 meters/min
:)

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