Math Problem Statement
A truck goes M to N at an average speed of 60km/h . The journey takes 30hrs. It returns from N to M on the same road with an average speed of 40km/h . What was the average speed of the truck during the whole journey in m/s ?
Solution
To calculate the average speed of the truck during the whole journey in meters per second (m/s), we follow these steps:
Step 1: Total Distance Calculation
The truck's journey consists of two parts:
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From to :
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From to : Since the truck returns on the same road, the distance is the same: .
The total distance for the whole journey:
Step 2: Total Time Calculation
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Time taken from to :
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Time taken from to :
The total time for the whole journey:
Step 3: Average Speed Calculation
The average speed of the whole journey is calculated using the formula:
In kilometers per hour:
Convert this to meters per second ():
Final Answer:
The average speed of the truck during the whole journey is:
Would you like further clarification or more details? Here are related questions to deepen your understanding:
- What is the formula for converting km/h to m/s?
- How does the time taken affect the average speed in cases of varying speeds?
- What would the average speed be if the truck's return speed was 60 km/h instead of 40 km/h?
- Can you explain why the average speed is not the arithmetic mean of 60 km/h and 40 km/h?
- How would the calculation change if the truck traveled different distances for the two legs of the journey?
Tip: Always remember that the average speed for a round trip is determined by the total distance divided by the total time, not the arithmetic mean of the speeds.
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Math Problem Analysis
Mathematical Concepts
Average Speed
Unit Conversion
Distance-Time-Speed Relationship
Formulas
Total Distance = Distance (M to N) + Distance (N to M)
Total Time = Time (M to N) + Time (N to M)
Average Speed = Total Distance / Total Time
Conversion from km/h to m/s: 1 km/h = 5/18 m/s
Theorems
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Suitable Grade Level
Grades 8-10