Concept explainers
A plane leaves Chicago and flies 750 miles to New York. It it takes 2.5 hours to get to New York flying against the wind, but only 2 hours to fly back to Chicago, what is the plane’s rate of speed and what is the wind speed?
To find the plane’s rate of speed and the wind speed
Answer to Problem 18P
Speed of plane is 337.5 miles per hour
Speed of wind is 37.5 miles per hour
Explanation of Solution
Given:
Distance between Chicago and New York is 750 miles
Formula Used:
Calculation:
Let,
The speed of the plane be
The speed of wind be
Now, the net speed of plane while going from Chicago to New York while flying against the wind is
And, the net speed of plane while going from New York to Chicago while flying along the wind is
Since, it takes
Also, it takes 2 hours to fly from New York to Chicago, therefore,
Let,
Now, adding equation ( i ) and ( ii ),
Substituting the value of
Conclusion:
Hence, the speed of plane is 337.5 miles per hour and speed of wind is 37.5 miles per hour.
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