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?
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?
Como
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
?
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_lender
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).