Example: Finding Travel Time for Pierre and Monique Moving in Opposite Directions
Apply the distance, rate, and time problem-solving strategy to find the unknown travel time when two people depart from the same point and move in opposite directions.
Problem: Pierre and Monique leave their home in Portland at the same time. Pierre drives north on the turnpike at a speed of miles per hour while Monique drives south at a speed of miles per hour. How long will it take them to be miles apart?
- Read and draw: Sketch the situation with arrows pointing north ( mph) and south ( mph), and label the total separation as miles. Create a rate–time–distance table.
- Identify: The travel time until they are miles apart.
- Name: Let = the travel time in hours. Multiply each rate by to fill in the distance column:
| Rate (mph) | Time (hrs) | Distance (miles) | |
|---|---|---|---|
| Pierre | |||
| Monique | |||
- Translate: Because they travel in opposite directions from the same starting point, the distance between them is the sum of their individual distances:
- Solve: Combine like terms: . Divide both sides by : .
- Check: Pierre's distance: miles. Monique's distance: miles. Total distance: miles.
- Answer: It will take them hours to be miles apart.
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Example: Finding Travel Time for Pierre and Monique Moving in Opposite Directions
Example: Finding Travel Time for Thanh and Nhat Moving in Opposite Directions