Question

A tortoise travels 11 feet in one hour. In each subsequent hour, the tortoise travels one-third the distance it traveled in the previous hour. How far does this tortoise travel in 6 hours?

Answer 1

16.5.......................

Answer 2

Answer:

The distance that a tortoise will cover in 6 hours is:

                        16.47735 feet.

Step-by-step explanation:

It is given that :

A tortoise travels 11 feet in one hour.

In each subsequent hour, the tortoise travels one-third the distance it traveled in the previous hour.

• This means that in 2 hours it travels a total of:

$11+\dfrac{1}{3}\times 11\ feet$

which is equal to:

$11\times \dfrac{4}{3}\ feet=\dfrac{44}{3}\ feet$

• in the 3 hours it will travel a total of:

$=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11\ feet$

• In 4 hours it will travel a total of:

$=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11\ feet$

• In 5 hours it will travel a total of:

$=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11\ feet$

• In 6 hours it will travel a total of:

$=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11+\dfrac{1}{3^5}\times 11\ feet=16.47735\ feet$

                     Hence, the answer is:

                               16.47735 feet