SOLUTION: A and B start together from the same point on a circular track and walk in the same direction till they both again arrive together at the starting point. A completes one circle in
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Question 930764: A and B start together from the same point on a circular track and walk in the same direction till they both again arrive together at the starting point. A completes one circle in 224 s and B in 364 s. How many times will A have passed B?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
For A and B to arrive together at the starting point,
each of them must have completed an integer number of turns.
The time (in seconds) required for that must be a multiple of and of .
and , so
the minimum common multiple of and is
.
That means that A and B first arrive together at the starting point seconds after the start.
During that time, A will have run laps,
and will have run laps.
Each time the distance A has run exceeds the distance B has run by an integer (1, 2, 3, or 4 laps), A is passing B.
When both have run for , A has run more laps than B, and they are both arriving together at the starting point.
I do not count that time as A passing B,
because they both stop running at that point,
so A passes B .
A MORE DYNAMIC VIEW (in case you do not visualize it yet):
During their run, A is running at a speed of ,
while B is running at a speed of .
The difference in the distance they have both covered increases at a rate of
,
which means .
A will be passing B for the first time when he has run more than B,
which will take .
When they meet at the starting point, after , A will have run
more than B,
meaning that A will pass B during the they both run before meeting again
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