Question 1197567
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w = speed of the wind in mph


2 hrs + 48 min = 2 hrs + (48/60) hrs
2 hrs + 48 min = 2 hrs + 0.8 hrs
2 hrs + 48 min = 2.8 hrs


150-w = speed of the plane going against the wind
distance = rate*time
distance = (150-w)*2.8
distance = 420-2.8w


150+w = speed of the plane going with the wind
distance = rate*time
distance = (150+w)*2
distance = 300+2w


The distance is same each time because the plane is following the same route, when going from  Atlanta to Charleston then back from Charleston to Atlanta.


Because the distance is the same for each equation, we can equate the right hand sides and solve for w.
420-2.8w = 300+2w
420-300 = 2w+2.8w 
120 = 4.8w 
w = 120/4.8
w = 25
The speed of the wind is 25 mph


Check:
If the plane goes against the wind, then its speed is 150-w = 150-25 = 125 mph. 
Traveling for 2.8 hours means it covers a distance of 125*2.8 = 350 miles
If the plane goes with the wind, then its speed is 150+w = 150+25 = 175 mph. 
Traveling for 2 hours gives a distance of 175*2 = 350 miles.
We get the same distance each time to help confirm the answer.


Answer: <font color=red>25 mph</font>
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