SOLUTION: Hope someone can help quick - I have a test on Monday and am having terrible difficulty with the story probs. Here's one problem: "Plane took 1 hr. LONGER to fly 480 AGAINST the

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Question 58613This question is from textbook Elementary Algebra
: Hope someone can help quick - I have a test on Monday and am having terrible difficulty with the story probs.
Here's one problem: "Plane took 1 hr. LONGER to fly 480 AGAINST the wind than it took to fly the same distance WITH the wind. If wind speed is 20 mph, what is the speed of plane in calm air?" I don't know how to figure speed of plane just based on air speed. All I know is distance is 480 both ways and time taken is "x + 1" for against wind and "x" for with wind. Can you help?
 This question is from textbook Elementary Algebra

Found 2 solutions by Paul, uma:
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
EQUATION:
480%2F%28x-20%29-480%2F%28x%2B20%29=1
480((x+20)-(x-20))=(x-20)(x+20)
480%2840%29=x%5E2-400
19200%2B400=x%5E2
x=140
Hence, the speed of the plane is 140mph.
Paul.

Answer by uma(370) About Me  (Show Source):
You can put this solution on YOUR website!
Let the speed of the plane in calm air be x mph
With the wind speed of the plane = (x+20)mph
Against the wind speed of the plane = (x-20) mph
Time taken to travel 480 miles with the wind = 480 / (x + 20) hrs
Time taken to travel 480 miles against the wind = 480 / (x - 20) hrs
Therefore according to the problem,
480/(x-20) - 480/ (x+20) = 1
==> 480x + 9600 -480x + 9600 = x^2 - 400
==> 19600 = x^2
==> x = 140
Therefore the speed of the plane = 140 mph