Respuesta :
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:
[tex]11+\dfrac{1}{3}\times 11\ feet[/tex]
which is equal to:
[tex]11\times \dfrac{4}{3}\ feet=\dfrac{44}{3}\ feet[/tex]
- in the 3 hours it will travel a total of:
[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11\ feet[/tex]
- In 4 hours it will travel a total of:
[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11\ feet[/tex]
- In 5 hours it will travel a total of:
[tex]=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[/tex]
- In 6 hours it will travel a total of:
[tex]=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[/tex]
Hence, the answer is:
16.47735 feet
