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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 .

Let represent the distance both traveled and represent the time Jan traveled.

Equation for Carol: where d is the distance Carol and Jan traveled and is the time Carol walked.

Equation for Jan: where is distance Carol and Jan traveled and is time Jan biked.

Set both equations equal to each other because they traveled the same distance, just at different times.

Solve for .