Question 456076: a plane leaves ny and heads for chicago which is 750 miles away. the plane flying against the wind takes 2.5 hrs to reach chicago. after refueling, the plane returns to ny in 2 hrs, traveling with the wind. find the speed of the wind and the speed of the plane with no wind.
Found 2 solutions by oberobic, Alan3354:
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! d = rt
distance = rate * time
d = 750
r = rate of speed
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s = speed with no wind (that is, in calm air)
w = wind speed
Going against the wind, r = s-w
Going with the wind, r = s+w
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It takes 2.5 hours to travel the 750 miles against the wind.
750 = r * 2.5
r = s-w
750 = (s-w) * 2.5
750 = 2.5s -2.5w
Multiply by 10 to remove the decimal points.
7500 = 25s -25w
Divide both sides by 25
300 = s -w
Add w to both sides
300+w = s
s = 300+w
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It takes 2 hours to travel the 750 miles with the wind.
750 = r * 2
r = s+w
750 = (s+w) * 2
750 = 2s + 2w
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Substitute s = 300+w
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750 = 2(300+w) +2w
750 = 600 +2w +2w
750 = 600 +4w
Subtract 600 from both sides
150 = 4w
Divide both sides by 4
37.5 = w
w = 37.5
The wind speed is 37.5.
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Substitute this value in the other equation to find s.
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750 = 2s + 2w
750 = 2s + 2*37.5
750 = 2s + 75
Subtract 75 from both sides
675 = 2s
2s = 675
Divide both sides by 2.
s = 337.5
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Always check your answer
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Flying TO Chicago, r = 337.5 - 37.5 = 300
The distance = 750
750 = 300*t
t = 2.5
Correct
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Flying FROM Chicago, r = 337.5 + 37.5 = 375
The distance = 750
750 = 375 * t
t = 2
Correct.
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Re-read the question to make sure you answer it.
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The speed of the wind is 37.5 miles per hour. (Remember to state the units.)
The speed of the airplane with no wind is 337.5 mph.
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Done.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! a plane leaves ny and heads for chicago which is 750 miles away. the plane flying against the wind takes 2.5 hrs to reach chicago. after refueling, the plane returns to ny in 2 hrs, traveling with the wind. find the speed of the wind and the speed of the plane with no wind.
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750/2.5 = 300 mph
750/2 = 375 mph
The plane's airspeed is the average = (300 + 375)/2 = 337.5 mph
The windspeed is the difference = 337.5 - 300 = 37.5 mph
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