The average airspeed of a single engine aircraft is 150...

Name: Problem 66, Chapter 12: Algebra and Trigonometry
Uploaded: 2020-11-29T14:20:43-08:00
Duration: 1 min 39 s
Channel: Dharmendra Jain
Description: The average airspeed of a single engine aircraft is 150 miles per hour. If the aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind, what was the wind speed?

The average airspeed of a single engine aircraft is 150 miles per hour. If the aircraft flew the same distance in 2 hours with the wind as it flew in 3 hours against the wind, what was the wind speed?

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Key Concepts

Relative Speed

Relative speed involves the concept of combining the speeds of two moving entities, in this case, the aircraft's airspeed and the wind speed, to determine the effective ground speed. When moving with the wind, the speeds add; when moving against the wind, they subtract, influencing the total distance covered in a given time.

Distance-Time Relationship

The distance-time relationship is a fundamental concept stating that distance equals speed multiplied by time. This relationship is used to calculate the distance traveled by the aircraft in both scenarios, given varying effective speeds due to the wind's effect.

System of Equations

When the same distance is covered under different conditions (with the wind and against the wind) in respective times, two equations with the same distance can be set up. Equating these expressions creates a system of equations that can be solved to find the unknown wind speed.

Algebraic Manipulation

Algebraic manipulation involves rearranging and simplifying equations to isolate and solve for the unknown variable. In the context of this problem, it is used to solve for the wind speed by equating and simplifying the equations derived from the distance-time relationship.

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