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?

Guest Feb 23, 2020

#1**+1 **

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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Guest 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** )

Check the answer:

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