Problema Solution
When a plane flies with the wind, it can fly 896 miles in 4 hours. When the plane flies in the opposite direction, against the wind, it takes 7 hours to fly the same distance. What is the average velocity of the wind?
Answer provided by our tutors
Let
d = 896 mi the distance traveled in each direction
t1 = 4 hr traveling with the wind
t2 = 7 hr traveling against the wind
w = the speed of the wind
v = the speed of the plane in still air
since average speed = distance/time we have:
traveling with the wind the speed of the plane is: v + w
v + w = d/t1
v + w = 896/4
v + w = 224
traveling against the wind the speed of the plane is: v - w
v - w = d/t2
v - w = 896/7
v - w = 128
by solving the system of equations:
v + w = 224
v - w = 128
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v = 176 mph
w = 48 mph
The average velocity of the wind is 48 mph.