Question

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?

Answer 1

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:
`x-(2)/(5)`.

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

Since we know that
`\text{Time}=\frac{\text{Distance}}{\text{Speed}}`, so we can set two equations for time taken by Achilles and turtle as:

`t=(x)/(13)...(1)`

`t=((x-(2)/(5)))/(1)...(2)`

From equation (1) we will get,

`x=13t`

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

`t=(13t-(2)/(5))/(1)`

Let us have a common denominator.

`t=((65t-2)/(5))/(1)`

`t=(65t-2)/(5)`

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

`5t=5* (65t-2)/(5)`

`5t=65t-2`

`5t-65t=65t-65t-2`

`-60t=-2`

`t=(-2)/(-60)`

`t=(1)/(30)`

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

`(1)/(30)\text{ hour}* \frac{60\text{ minutes}}{\text{hour}}`

`(1)/(30)* 60\text{ minutes}`

`2\text{ minutes}`

Therefore, the competition took 2 minutes.