A car travels at a speed of 60 km/h and then at 80 km/h, covering a total distance of 280 km in 4 hours. How long did it travel at 60 km/h? - Abbey Badges
How Long Did the Car Travel at 60 km/h and 80 km/h? Solve This Distance & Time Problem
How Long Did the Car Travel at 60 km/h and 80 km/h? Solve This Distance & Time Problem
When faced with a scenario where a car travels part of a journey at 60 km/h and the rest at 80 km/h, determining how long the car moved at each speed can seem tricky—but with the right approach, it’s straightforward. Let’s break down a classic problem where a car covers a total of 280 km in 4 hours, moving first at 60 km/h and later at 80 km/h. The key is setting up equations based on distance, speed, and time.
Problem Recap:
- Total distance: 280 km
- Total time: 4 hours
- Speeds: 60 km/h and 80 km/h
- Unknown: Time traveled at 60 km/h (call this time t hours)
- Therefore, time traveled at 80 km/h = (4 – t) hours
Understanding the Context
Step 1: Express Distances Using Speed × Time
Distance = Speed × Time
Let time at 60 km/h be t → Distance = 60 × t = 60t
Let time at 80 km/h be (4 – t) → Distance = 80 × (4 – t) = 80(4 – t)
Step 2: Set Up the Total Distance Equation
Total distance = 60t + 80(4 – t) = 280
Now solve for t:
60t + 320 – 80t = 280
Combine like terms:
–20t + 320 = 280
Subtract 320 from both sides:
–20t = –40
Divide by –20:
t = 2
Conclusion:
The car traveled at 60 km/h for 2 hours, and at 80 km/h for the remaining 2 hours (since 4 – 2 = 2). This satisfies both the total time and total distance conditions.
Bonus: Verify the Distances
– At 60 km/h for 2 hours: 60 × 2 = 120 km
– At 80 km/h for 2 hours: 80 × 2 = 160 km
Total = 120 + 160 = 280 km — correct!
Time used: 2 + 2 = 4 hours — matches the given total time.
Key Insights
This problem illustrates how algebraic reasoning helps solve real-world speed, distance, and time puzzles. Whether you're analyzing traffic patterns or planning a road trip, understanding these relationships is invaluable. Use this method whenever you need to break down multistage journeys into manageable math.
Keywords: car speed problem, distance and time, physics equations, solving speed-time-distance, car travel problem 60 to 80 km/h, how long traveled at 60 km/h, mathematics problem solving
