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Problem-Solving Strategy for Distance, Rate, and Time Applications
When a uniform motion problem involves two travelers or vehicles, the general formula-based strategy is enhanced with visual and organizational tools. The adapted seven-step process is:
- Read the problem and make sure all the words and ideas are understood.
- Draw a diagram to illustrate the situation (e.g., sketch the route with labeled arrows for each traveler).
- Create a table with columns for Rate, Time, and Distance, and one row for each scenario.
- Fill in the information that is given.
- Identify what you are looking for.
- Name the unknown by choosing a variable, then complete the table. Use variable expressions to represent unknown quantities in each row, and multiply rate by time to fill in the distance column (since ).
- Translate into an equation by restating the relationship between the two distances in one sentence, then converting that sentence into an equation.
- Solve the equation using standard algebra techniques.
- Check the answer in the original problem to make sure it is reasonable.
- Answer the question with a complete sentence.
The key adaptations for distance, rate, and time problems are the diagram and the rate–time–distance table, which organize the two-scenario information visually and make it straightforward to identify the equation connecting the distances.
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Learn After
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