Hi,

I'm working on a problem right now that involves the story about the race between the tortoise and the hare, and I'm having some trouble.

The race is 2000m. The tortoise travels 20m per minute, and the hare travels 1000m in the first minute and half the remaining distance per minute after that. Right away this question seems odd because by definition, the hare will never finish the race if it is always going half the remaining distance. But anyway, I'm asked to write the series for both the tortoise and the hare, and I'm told specifically "each term of the series represents the distance the tortoise/hare travelsin that minute."

So by what they're asking, the series for the tortoise would be:

20 + 20 + 20 + 20....

a = 20 d = 0

and the hare:

1000 + 500 + 250 + 125....

a = 1000 r = 0.5

I am then asked to find formulas for Sn for both the tortoise and the hare, where Sn represents the total distance travelled after n minutes.

For the tortoise, it doesn't seem to fit the equation we have learned for arithmetic series': Sn = n/2[2a + (n - 1)d]/2 it seems the most fitting equation is just: Sn = 20n

For the hare, the equation Sn = [1000(1 - 0.5^n)]/0.5 seems to work just fine

Could somebody please help me with this? I'm not sure if I'm doing something wrong, or if my equations are wrong, or anything. The strangeness of the question just has my mind all mixed up. I know by definition the hare cannot finish the race, and the tortoise finishes after 100 minutes (simple math), but this all can't be that easy. Can it?

Thanks very much