The tortoise and the hare are in a road race to defend the honor of their breed. The tortoise crawls the

Question

 Sorry here is the rest of the question

- entire 1000 m distance at a speed of 0.2000 m/s while the rabbit runs the first 200.0 m at 2.000 m/s. The rabbit the stops to take a nap for 1.300 hr and awakens to finish the last 800.0 m with an average speed of 3.000 m/s. Who wins the race and by how much time?

Answer 1

Hi Makayla--

 

The key is to turn everything into seconds, of course.

 

Tortoise goes 1000 meters at .2 meters per second. Each full meter is 5 times greater than .2, which means it takes tortoise 5 seconds per full meter, or 5000 seconds, to finish the race.

 

Now, onto Mr. Hare (who is going to lose, btw--everyone knows this story!):

 

Using the same kind of math as above, we can figure that his first sprint will take him just 400 seconds. (2 meters per second, times 200 meters).

 

But the nap kills his chances--if he naps for 1 and 3/10 of an hour, that's an hour and 18 minutes. (one-tenth of an hour is 6 minutes, x 3 = 18 minutes.

 

1 hour and 18 minutes = 78 minutes, x 60 seconds = 4680 seconds JUST FOR THE NAP!

 

Then he finishes the race with another sprint of 2400 seconds, because it's 800 meters at 3 meters per second.

 

Add up all of Hare's times: 2400 + 4680 + 400 = 7480 seconds, and remember that slow-and-steady tortoise took just 5000 seconds.

 

Which means tortoise won by ... 2480 seconds, which in more manageable numbers would be ... 41 minutes and 20 seconds.

 

Cool question!

 

Matt in New York

 

PS: I bet at least one person in your class will confuse "1.3 hours" with "1 and a third hours," and they'll think that Hare napped for an hour and _20_ minutes--but YOU'LL be right!