### Home > INT1 > Chapter 8 > Lesson 8.1.2 > Problem8-30

8-30.

Carol and Jan leave from the same place and travel on the same road going the same direction. Carol walks at a rate of two miles per hour. Carol left five hours earlier than Jan, but Jan bikes at a rate of six miles per hour. How far did they travel when Jan caught up to Carol?

Visualize the problem by drawing a picture of the situation and remember $d = rt$.

Let $d$ represent the distance both traveled and $t$ represent the time Jan traveled.

Equation for Carol: $d = 2(t + 5)$ where d is the distance Carol and Jan traveled and $t + 5$ is the time Carol walked.

Equation for Jan: $d = 6t$ where $d$ is distance Carol and Jan traveled and $t$ is time Jan biked.

Set both equations equal to each other because they traveled the same distance, just at different times.
$2(t + 5) = 6t$
Solve for $t$.