SOLUTION: A plane flying with the jet stream flew from los angeles to chicago, a distance of 2250 mi, in 5 h. Flying against the jet stream, the plane could fly only 1750 mi in the same amou

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Question 538848: A plane flying with the jet stream flew from los angeles to chicago, a distance of 2250 mi, in 5 h. Flying against the jet stream, the plane could fly only 1750 mi in the same amount of time. Find the rate of the plane in calm air and the rate of the wind.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
a = airspeed
w = wind speed
.
(a+w)*5 hr = 2250 miles
.
(a-w)*5 hr = 1750 miles
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Using the distributive property to eliminate the parentheses.
Then solve the system of equations by elimination
.
5a + 5w = 2250
5a - 5w = 1750
--------------- add
10a = 4000
.
a = 400
.
Substitute a = 400 to find 'w'.
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5(400) + 5w = 2250
2000 + 5w = 2250
5w = 250
w = 50
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Check the distances traveled in 5 hr to make sure these answers are right.
(400+50)*5 = 2250
(400-50)*5 = 1750
Correct.
.
Answer: Airspeed in calm air is 400 mph. The wind speed is 50 mph.
.
Done.