# 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.

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.