To find:the wind speed and the air speed of the helicopter.
Answer to Problem 7P
The wind speed and the air speed of the helicopter are 15 miles per hour and 165 miles per hour, respectively.
Explanation of Solution
Given information:
With a tail wind, a helicopter traveled 300 mi in 1 hour 40 min.
The return trip against the same wind took 20 min longer.
Calculation:
Let x be speed of wind and let y be the air speed of the helicopter.
With a tail wind, the ground speed is
In the return trip, the ground speed is
Note that, the distance traveled by helicopter is multiplication of ground of speed and time.
With tail wind, the helicopter traveled 300 mi in 1 hour 40 min.
The return trip against the same wind took 20 min longer.
Thus, the helicopter traveled 300 mi in 2 hour when the return trip.
Divide on both sides by 2,
Compute the solutions of the system
Multiply the equation
Add two equations
Divide on both sides by10,
Substitute
Therefore, the wind speed and the air speed of the helicopter are 15 miles per hour and 165 miles per hour, respectively.
Chapter 3 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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