SOLUTION: An airplane flying against the wind travels 300 miles in the same time that it takes the same plane to travel 400 miles with the wind. If the wind speed is 20 miles per hour, find

Question 949795: An airplane flying against the wind travels 300 miles in the same time that it takes the same plane to travel 400 miles with the wind. If the wind speed is 20 miles per hour, find the speed of the airplane in still air.
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
r=rate of plane in still air
300 miles/r-20mph=400 miles/r+20 mph Multiply each side by(r-20mph)
300 miles= 400 mi(r-20 mph)/r+20 mph Multiply each side by (r+20 mph)
300 miles(r+20 mph)=400 miles(r-20 mph)
300r+6000mph=400r-8000mph Add 8000mph to each side.
300r+14000mph=400r Subtract 300r from each side.
14000mph=100r Divide each side by 100.
140 mph=r ANSWER: The rate of the plane in still air would be 140 mph
CHECK:
300 mi/140mph-20mph=400 mi/140mph+20mph
300mi/120mph=400mi/160mph
2.5 hrs=2.5 hrs

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