Question

The turtle and Achillies compete. They start at the same time from the same place. Achillies runs at a speed of 13 mph and the turtle runs at a speed of 1 mph. When Achillies reached the finish line the turtle was 2/5 behind him. How long was the distance between the start and the finish line

Answer 1

Answer:

$Distance=\frac{13}{30}\ miles$

Step-by-step explanation:

Let Achillies completed the distance in $t\ hours$.

$distance(s)=speed\times time\\\\s=13\times t=13t\\\\In\ t\ hours\ distance\ covered\ by\ turtle=speed\ of\ turtle\times time=1\times t=t\\\\Turtle\ was\ \frac{2}{5}\ of\ total\ mile\ behind\ Achillies\\\\s-t=\frac{2}{5}\\\\s-\frac{s}{13}=\frac{2}{5}\ \ \ \ \ \ \ (as\ s=13t\Rightarrow t=\frac{s}{13})\\\\\frac{12}{13}s=\frac{2}{5}\\\\s=\frac{13}{30}\ miles$