Question 556130: You fly from LAX to NYC. It takes 5.6 hours to travel 2100 miles against the head wind. At the same time, your friend flies from LAX to NYC. Their plan travels with the same average airspeed but with a tail wind, her flight takes only 4.8 hours. Find the airspeed and the windspeed.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance.
let p = speed of plane and let w = speed of wind
going with the wind, the speed of the wind adds to the speed of the plane.
going against the wind, the speed of the wind subtracts from the speed of the plane.
your equations are:
5.6*(p-w) = 2100
4.8*(p+w) = 2100
simplify these equations to get:
5.6*p - 5.6*w = 2100
4.8*p + 4.8*w = 2100
multiply the first equation by 4.8 and multiply the second equation by 5.6 to get:
4.8*5.6*p - 4.8*5.6*w = 4.8*2100
4.8*5.6*p + 4.8*5.6*w = 5.6*2100
add these 2 equations together to get:
2*(4.8*5.6*p) = 2100*(4.8+5.6)
simplify to get:
53.76*p = 21840
divide both sides of this equation by 53.76 to get:
p = 406.25
the speed of the plane is 406.25 miles per hour.
going with the wind, the equation of:
4.8*(p+w) = 2100 becomes:
4.8*(406.25+w) = 2100 which becomes:
4.8*406.25 + 4.8*w = 2100
simplify to get:
1950 + 4.8*w = 2100
subtract 1950 from both sides of the equation and then divide both sides of the equation by 4.8 to get:
w = 31.25 miles per hour.
you now have:
p = 406.25
w = 31.25
substitute these values in the going against the wind equation of
5.6*(p-w) = 2100 to get:
5.6*(406.25-31.25) = 2100 which becomes:
5.6*375 = 2100 which becomes:
2100 = 2100
this confirms the values of p = 406.25 and w = 31.25 are good.
speed of the plane is 406.25 miles per hour.
speed of the wind is 31.25 miles per hour.
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