Problema Solution
Against the wind a commercial airline in South America flew 216 miles in 2 hours. With a tailwind the return trip took 1.5 hours. What was the speed of the plane in still air? What was the speed of the wind?
Answer provided by our tutors
Let
d = 216 mi the distance traveled in each direction
t1 = 2 hr traveling against the wind
t2 = 1.5 hr traveling with the wind (tailwind)
w = the speed of the wind
v = the speed of the plane in still air
Since speed = distance/time we have:
Traveling against the wind the speed of the plane is: v - w
v - w = d/t1
v - w = 216/2
v - w = 108
Traveling with the wind the speed of the plane is: v + w
v + w = 216/1.5
v + w = 144
We need to solve the following system of equations:
v - w = 108
v + w = 144
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click here to see the system of equations solved for x and y
........
v = 126 mph
w = 18 mph
The speed of the wind is 18 mph.
The speed of the plane in still air is 126 mph.