Solving a Catch-Up Uniform Motion Problem Where One Driver Leaves 1 Hour Later
Apply the seven-step problem-solving strategy for systems of linear equations to a uniform motion catch-up scenario, using two variables and substitution to solve the resulting system.
Problem: Mitchell left Detroit on the interstate driving south towards Orlando at a speed of miles per hour. Clark left Detroit hour later traveling at a speed of miles per hour, following the same route as Mitchell. How long will it take Clark to catch Mitchell?
- Read the problem and draw a diagram showing both drivers traveling the same route from Detroit to Orlando. Create a rate–time–distance table.
- Identify: The travel time for each driver.
- Name: Let = Mitchell's driving time (in hours) and = Clark's driving time (in hours). Identify the rates: Mitchell's rate is mph, Clark's rate is mph. Multiply rate by time to fill in the distance column:
| Rate (mph) | Time (hrs) | Distance (miles) | |
|---|---|---|---|
| Mitchell | |||
| Clark |
- Translate into a system of equations. Clark catches Mitchell when they have traveled the same distance: . Since Clark left hour later, his time is hour less than Mitchell's: . The system is:
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Solving a Catch-Up Uniform Motion Problem Where One Driver Leaves 1 Hour Later
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