Question

A snail travels 2 feet in 1 hour. In each subsequent hour, the snail travels two-thirds the distance it traveled in the previous hour. How far does this snail travel in 8 hours? Round your answer to the nearest tenth.

Answer 1

Answer:

The

Explanations:

The distance travelled by the snail in 1 hour = 2 feet

Let the distance travelled in 1 hour be represented by d₁

d₁ = 2 feet

The snail travelled two-thirds the distance it travelled in the previous hour

This means that the common ratio of the distance travelled is 2/3

Let the common ratio be represented as r

r = 2/3

Since the distance travelled by the snail in subsequent hours has a common ratio, r, this scenario can be modelled by the sum of n terms in a Geometric Progression.

The distance travelled by the snail in n hours will be given as:

$S_n=\text{ }\frac{d_1(r^n-1)}{r-1}$

The distance travelled by the snail in 8 hours will be calculated by substituting n = 8 into the equation above:

$\begin{gathered} S_8=\frac{2\lbrack(\frac{2}{3})^8-1\rbrack}{\frac{2}{3}-1} \\ S_8=\text{ }\frac{2(0.039-1)}{0.67-1} \\ S_8=\text{ }\frac{2(-0.961)}{-0.33} \\ S_8=\text{ }\frac{-1.922}{-0.33} \\ S_8=5.8 \end{gathered}$

The distance travelled in 8 hours is 5.8 feet