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 long is the distace from start to finish

0.43 miles

Step-by-step explanation:

Let t be the time it takes Achilles to run the race. Since Achilles runs at a speed of 13 mph, the distance he covers in time t is d = 13t.

Also, by the time Achilles finishes the race, the turtle has already covered a distance, d at a speed of 1 mph in the same time, t. So, d' = 1t = t

Given that when Achilles reaches the finish line, the turtle is 2/5 of a mile behind him, then d - d' = 2/5.

So, 13t - t = 2/5

12t = 2/5

t = 2/5 × 1/12

t = 1/5 × 1/6

t = 1/30 h

So since d = distance from start to finish = distance Achilles covers = 13t,

Substituting t = 1/30 into d, we have

d = 13t

= 13 × 1/30

= 0.43 miles

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