# Spongebob and Patrick are running away from the Krusty Krab. Spongebob runs east at 4 feet per second while Patrick runs west at 2 feet per second. How long will it take them to be 192 feet apart?

Sep 24, 2015

For the time being, we can ignore the signs of their velocities, but rather add their speeds. So the total speed we can say is

$4 + 2 = 6 \frac{f t}{s}$

We are trying to find the time, so we can set up a proportion:

$\frac{6 f t}{s} = \frac{192 f t}{x s}$

which gives us $x = 32 s$

We can check by multiplying the time by their individual velocities:
Spongebob: $32 \cancel{s} \cdot 4 \frac{f t}{\cancel{s}} = 128 f t$ to the right
Patrick: $32 \cancel{s} \cdot 2 \frac{f t}{\cancel{s}} = 64 f t$ to the left
When you add these two together you find $192 f t$.