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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?

Respuesta :

frika

Answer:

[tex]\dfrac{13}{30}\ mile[/tex]

Step-by-step explanation:

Achilles:

Rate = 13 mph

Time = t hours

Distance = D miles

Then

[tex]D=13\cdot t[/tex]

Turtle:

Rate = 1 mph

Time = t hours

Distance [tex]=D-\dfrac{2}{5}[/tex] miles

Then

[tex]D-\dfrac{2}{5}=1\cdot t[/tex]

Hence,

[tex]t=D-\dfrac{2}{5}[/tex]

and

[tex]D=13\cdot \left(D-\dfrac{2}{5}\right)\\ \\D=13D-\dfrac{26}{5}\\ \\13D-D=\dfrac{26}{5}\\ \\12D=\dfrac{26}{5}\\ \\D=\dfrac{26}{60}=\dfrac{13}{30}\ mile[/tex]