Problema Solution
Against the wind a small plane flew 210 miles in one hour and 10 minutes. The return trip took only 50 minutes. What was the speed of the wind? What was the speed of the plane in still air?
Answer provided by our tutors
let
v = the speed of the plane in still air
w = the speed of the wind
d = the distance in one direction
t1 = 10 min = 10/60 h = 1/6 h the time flying against the wind
t2 = 50 min = 50/50 = 5/6 h the time flying with the wind
the speed of the plane against the wind v - w
the speed of the plane with the wind v + w
speed = distance/time => distance = speed*time
Against the wind a small plane flew 210 miles in one hour and 10 minutes
v - w = 210
d = (v - w)*t1
d = 210*(1/6)
The return trip took only 50 minutes
d = (v + w)*t2
d= (v + w)*(5/6)
(v + w)*(5/6) = 210*(1/6) multiply both sides by 6
(v + e)*5 = 210
by solving the system of equations
v - w = 210
(v + w)*5/6= 210
we find
v = 231 mph
w = 21 mph
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the speed of the plane in still air is 231 miles per hour.
the speed of the wind is 21 miles per hour.