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 long is the distance between the start line and the finish line?

Answer 1

`(13)/(30)\ mile`

Explanation:

Achilles:

Rate = 13 mph

Time = t hours

Distance = D miles

Then

`D=13\cdot t`

Turtle:

Rate = 1 mph

Time = t hours

Distance
`=D-(2)/(5)` miles

Then

`D-(2)/(5)=1\cdot t`

Hence,

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

and

`D=13\cdot \left(D-(2)/(5)\right)\\ \\D=13D-(26)/(5)\\ \\13D-D=(26)/(5)\\ \\12D=(26)/(5)\\ \\D=(26)/(60)=(13)/(30)\ mile`