SOLUTION: A plane traveled 924 miles to Seattle and back. The trip there was with the wind. It took 11 hours. The trip back was into the wind. The trip back took 22 hours. what is the speed

Question 928640: A plane traveled 924 miles to Seattle and back. The trip there was with the wind. It took 11 hours. The trip back was into the wind. The trip back took 22 hours. what is the speed of the plane in still air? What is the speed of the wind?
I have an answer but do not know if it is right. I got 63 mph is how fast the plane is going in still air and I got that the speed of the wind was 21 mph.
Found 4 solutions by TimothyLamb, stanbon, MathTherapy, Alan3354:
Answer by TimothyLamb(4379)   (Show Source): You can put this solution on YOUR website!
x = speed of airplane in still air
y = speed of wind
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s = d/t
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with the wind:
x + y = 924/11
x + y = 84
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against the wind:
x - y = 924/22
x - y = 42
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put the system of linear equations into standard form
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x + y = 84
x - y = 42
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copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution:
x = speed of airplane in still air = 63 mph
y = speed of wind = 21 mph
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
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Solve systems of linear equations up to 6-equations 6-variables:
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Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
A plane traveled 924 miles to Seattle and back. The trip there was with the wind. It took 11 hours. The trip back was into the wind. The trip back took 22 hours. what is the speed of the plane in still air? What is the speed of the wind?
--------------------
Trip back into wind DATA:
distance = 924 miles: time = 22 hrs ; rate = 924/22 = 42 mph
p - wind = 42 mph
Trip to Seattle with wind DATA:
distance = 924 miles; time = 11 hrs ; rate = 924/11 = 84 mph
p + wind = 84
----
Add the 2 equations to get:
2p = 126
plane = 58 mph
-----------------------
Subtract the 2 equations to get;
2w = 42
wind = 21 mph
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Cheers,
Stan H.
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I have an answer but do not know if it is right. I got 63 mph is how fast the plane is going in still air and I got that the speed of the wind was 21 mph.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

A plane traveled 924 miles to Seattle and back. The trip there was with the wind. It took 11 hours. The trip back was into the wind. The trip back took 22 hours. what is the speed of the plane in still air? What is the speed of the wind?
I have an answer but do not know if it is right. I got 63 mph is how fast the plane is going in still air and I got that the speed of the wind was 21 mph.

Let speed of plane, in still air, and speed of wind be S, and W, respectively
Average speed to Seattle: , or 84 mph
Traveling with the wind, we can say that: S + W = 84 ------ eq (i)
Average speed from Seattle: , or 42 mph
Traveling against the wind, we can say that: S - W = 42 ------ eq (ii)
2S = 126 ---------- Adding eqs (ii) & (i)
S, or speed of plane, in still air = , or mph
63 + W = 84 -------- Substituting 63 for S in eq (i)
W = 84 � 63
W, or speed of wind = mph
You�re 100% correct!! Good job!!
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
That's a really slow airplane.
A bus would be faster.
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