Question 107719This question is from textbook Introductory Algebra
: Question:
A plane flying with a tailwind flew 300 mi in 2 h. against the wind, it took 3h to travel the same distance. Find the rate of the plane in calm air and the rate of the wind.
**First list the two simultaneous equations using "W" for the wind speed and "P" for the speed of the plane. Identify the analytical method you will be using. (substitution or addition) describe the steps you use and list the solutions**
I'm lost with this question, thank you for your help.
This question is from textbook Introductory Algebra
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A plane flying with a tailwind flew 300 mi in 2 h. against the wind, it took 3h to travel the same distance. Find the rate of the plane in calm air and the rate of the wind.
**First list the two simultaneous equations using "W" for the wind speed and "P" for the speed of the plane. Identify the analytical method you will be using. (substitution or addition) describe the steps you use and list the solutions
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With the wind DATA:
distance = 300 miles ; Time = 2 hrs; rate = d/t = 300/2 = 150 mph
EQUATION: p + w = 150 mph
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Against the wind DATA:
distance = 300 miles ; Time = 3 hrs; rate = d/t = 300/3 = 100 mph
EQUATION: p - w = 100 mph
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Solve the system of equations by elimination.
Add the two equations to get:
2p = 250
p = 125 mph (plane's speed)
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Substitute into p+w = 150 to solve for w:
125 +w = 150
w = 25 mph ( wind speed)
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Cheers,
Stan H.
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