.
The relative speed is 500 - 5 = 495 yards per minute.
It is the rate of decreasing the distance between them, which initially was 990 yards.
Hence, the time to catching up is 
= 2 minutes.
It is how physicists solve such problems (momentarily !)
In Algebra, the canonical way is to write equations . . .
Let t be the time under the question.
Then the distance from the starting point of Achilles to the catching up point is 500*t yards.
The tortoise will cover 5t yards, and it is 990 yards less then Achilles will cover.
It gives you an equation
500t - 5t = 990,
which you can easily solve
495t = 990 ====> t = 990/495, by obtaining the same answer t= 2 minutes.
Solved.
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See introductory lessons on Travel and Distance problems
- Travel and Distance problems
- Travel and Distance problems for two bodies moving in opposite directions
- Travel and Distance problems for two bodies moving in the same direction (catching up)
in this site.
They are written specially for you.
You will find the solutions of many similar problems there.
Read them and learn once and for all from these lessons on how to solve simple Travel and Distance problems.
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