# The three-toed sloth is the slowest moving land mammal. On the ground, the sloth moves at an...

## Question:

The three-toed sloth is the slowest moving land mammal. On the ground, the sloth moves at an average speed of 0.0330 m/s, considerably slower than the giant tortoise, which walks at 0.0800 m/s. After 10.2 minutes of walking, how much further would the tortoise have gone relative to the sloth?

## Distance Between Two Moving Bodies

The distance between two moving bodies changes as time progresses. Since distance is path-dependent the path taken by the two is important. If they have different speed the gap between them increases as time progresses.

## Answer and Explanation:

Given:

- {eq}s_s = 0.0330\ \rm \frac{m}{s}{/eq} Speed of the sloth

- {eq}s_t = 0.0800\ \rm \frac{m}{s}{/eq} Speed of the tortoise

- {eq}t = 10.2\ \rm min = 612\ \rm s{/eq}

First, we solve for the distance covered by the sloth.

$$\begin{align} d_s &= s_st\\ d_s &= \left(0.0330\ \rm \frac{m}{s}\right)(612\ \rm s)\\ d_s &= 20.196\ \rm m \end{align} $$

Now we solve for the distance covered by the tortoise.

$$\begin{align} d_s &= s_st\\ d_s &= \left(0.0800\ \rm \frac{m}{s}\right)(612\ \rm s)\\ d_s &= 48.960\ \rm m \end{align} $$

Solving for the distance of the tortoise from the slot after 612 seconds.

$$\begin{align} d &= d_t - d_s\\ d &= 48.960\ \rm m - 20.196\ \rm m\\ d &= 28.764\ \rm m \end{align} $$

Therefore the distance of the tortoise from the sloth after 612 seconds is **28.764** m.

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#### Learn more about this topic:

from FTCE Mathematics 6-12 (026): Practice & Study Guide

Chapter 30 / Lesson 5