The turtle and achilles compete. they start at the same time from the same place. achilles runs at a speed of 13 mph while the turtle moves at a speed of 1 mph. when achilles reaches the finish line, the turtle is 2/5 of a mile behind him. how much time did the competition take?

2 minutes.  

Step-by-step explanation:

Let t be the time taken in competition and the distance covered by Achilles be x miles.

We have been given that when Achilles reaches the finish line, the Turtle is 2/5 of a mile behind him. This means that distance covered by turtle will be: .

Achilles runs at a speed of 13 mph while the Turtle moves at a speed of 1 mph.

Since we know that , so we can set two equations for time taken by Achilles and turtle as:

From equation (1) we will get,

Upon substituting this value in equation (2) we will get,

Let us have a common denominator.  

Upon multiplying both sides of our equation by 5 we will get,

So, the competition took 1/30 hour, let us convert our given time in minutes.

Therefore, the competition took 2 minutes.