Solving a Uniform Motion Application: Finding Travel Time for Trucks Moving in Opposite Directions
Apply the seven-step problem-solving strategy to determine the time required for two vehicles traveling in opposite directions to reach a specific separation distance.
Problem: Two truck drivers depart simultaneously from an interstate rest area. The westbound truck moves at mph, while the eastbound truck maintains an average speed of mph. How many hours will elapse before they are separated by miles?
- Read and draw: Sketch a diagram showing the rest stop with arrows indicating the westbound ( mph) and eastbound ( mph) trucks. The total separation is miles. Create a table with columns for Rate, Time, and Distance.
- Identify: We need to find the travel time until the trucks are miles apart.
- Name: Let equal the travel time in hours for both trucks. Multiply each vehicle's rate by to determine their individual distances. The westbound distance is and the eastbound distance is .
- Translate: Since the trucks are moving in opposite directions from the same starting point, the sum of their individual distances equals the total separation distance: .
- Solve: Combine the like terms to get . Dividing both sides by yields .
- Check: The westbound truck travels miles. The eastbound truck travels miles. The total distance is miles.
- Answer: The trucks will be miles apart after hours.
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