Math Problem Statement
Solution
The question reads:
A plane flew 4000 km downwind in 6 hours, then 4000 km upwind in 8 hours. What is the speed of the plane and the speed of the wind?
Let’s solve it step by step.
Variables:
- : Speed of the plane in still air (km/h)
- : Speed of the wind (km/h)
Downwind:
When flying downwind, the effective speed of the plane is: Using the formula: For the downwind leg:
Upwind:
When flying upwind, the effective speed of the plane is: Similarly, for the upwind leg:
Solve the System of Equations:
We now have two equations:
Adding the two equations:
Subtracting the second equation from the first:
Final Answer:
- Speed of the plane () = km/h
- Speed of the wind () = km/h
Would you like a detailed explanation of any step or more practice problems?
5 Related Questions:
- What is the formula for effective speed when traveling with or against the wind?
- How would the solution change if the distances were different?
- What happens if the wind speed is greater than the plane's speed in still air?
- Can you derive a general formula for problems of this type?
- How does the time of travel affect these types of problems?
Tip:
Always double-check units and ensure consistency between time, distance, and speed when solving these problems!
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Distance-Speed-Time Relationship
Formulas
Speed = Distance / Time
p + w = Downwind Speed
p - w = Upwind Speed
Theorems
Linear equation solving
Suitable Grade Level
Grade 10
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