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# Achilles and Turtles race

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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.

Chapter ReferenceExample

a

How much time did the competition take?

Feb 23, 2020

#1
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2/5 of a mile can be expressed as 0.4 of a mile.  Let's call it that, to make it easier for me.

We could do fractions, but decimals are easier.

Achilles runs at 13 mph, and Turtle at 0.4 mph.  So Achilles is outdistancing Turtle by 12.6 mph.

Do you see that?  In one hour, Achilles would have run 13.0 miles and Turtle would have run 0.4 mile.

Well, they didn't run for an entire hour, or Achilles would have been 12.6 miles ahead of Turtle.

How long did they run?  Distance = Speed x Time  ....  so let's start with that and see how far we get.

Consider that 0.4 mile.  They ran long enough for that to be the Distance.  Let's set it up.

D  =  S • T                                        (A "dot" means multiply.)

0.4 mile  =  (12.6 miles/hour) • T

Divide both sides by 12.6 miles/hour        (0.4 mile) • (12.6 miles/hour)  =  T

Doing the division, we find that                 T  =  0.0317 hour                             (A little less than 2 minutes.)

Why don't we go ahead and see if we can check that answer....

In 0.0317 hour, at 13 miles/hour, Achilles has run 0.412 mile

In 0.0317 hour, at 0.4 mile/hour, Turtle has run     0.013 mile

Subtract Turtle's distance from Achilles to confirm that Achilles is about 0.4 (aka 2/5) mile ahead.

The distance doesn't come out to exactly 0.4 because we did a little rounding along the way.

If you want a more precise answer, use a calculator and don't do any rounding.

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Feb 24, 2020
#2
+1

OMG I messed up and I can't edit.  Turtle doesn't run at 0.4 mph; Turtle runs at 1 mph.

I didn't copy the question like I usually do, and I wasn't glancing up at it as I worked through.

Evverywhere I referred to Turtle's speed as 0.4 mph above, change that to 1 mph.

So the calculation should be                  D  =  S • T

0.4 mile  =  (12 miles/hour) • T

(0.4 mile) / (12 miles/hour)  =  T

T  =  0.0333333 hour                  (i.e., 1/30 of an hour = 2 minutes

Achilles -  (1/30 of an hour) • (13 miles/hour)  =  0.4333 mile

Turtle    -  (1/30 of an hour) • (1 mile/hour)      =  0.0333 mile

So, we confirm that at the end of 1/30 of an hour, Achilles is 0.4 mile ahead of Turtle.

And I'm sorry for the error in my original answer;

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Guest Feb 24, 2020