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math question?
Against the wind a small plane flew 280 miles in 1 hour and 10 minutes. The return trip took only nothing50 minutes. What was the speed of the wind? What was the speed of the plane in still air?
3 Answers
- ComoLv 74 years ago
Let speed of wind = w mph
Let speed of plane in still air = x mph
______________With____Against
speed (mph)____x + w_____x - w
time (h)_________5/6_____7/6
distance (miles)__280____ 280
(5/6) (x + w) = 280
(7/6) (x - w) = 280
5x + 5w = 1680
7x - 7w = 1680
35x + 35w = 11760
35x - 35w = 8400_______add
70 x = 20160
x = 288
1440 + 5w = 1680
5w = 240
w = 48
Speed in still air = 288 mph
Wind speed = 48 mph
- TomVLv 74 years ago
Assuming the wind was directly aligned with the course:
280/(a-w) = 7/6 hour → a-w = 6(280)/7 = 240
280/(a+w) = 5/6 hour → a+w = 6(280)/5 = 336
2a = 576
a = 288
2w = 96
w = 48
Speed in still air = 288 mph
Wind speed = 48 mph
============================
- az_lenderLv 74 years ago
280 mi/70 min = 4 miles per minute.
280 mi/50 min = 5.6 miles per minute.
Plane speed - wind speed = 4.0 miles/minute;
Plane speed + wind speed = 5.6 miles/minute.
Evidently the plane speed (in still air) is 4.8 miles per minute (288 mph), and the wind speed is 0.8 miles per minute (48 mph).
