Question 104439This question is from textbook College Algebra
: This is a wind velocity problem. A plane can fly 340 miles per hour in still air. If it can fly 200 miles downwind in the same amount of time it can fly 140 miles upwind, find the velocity of the wind.
This question is from textbook College Algebra
Answer by stormy(4)   (Show Source):
You can put this solution on YOUR website! This problem is easily solved using the Distance formula, d=rt. It is helpful to set up a table with what you know.
Let w = the velocity of the wind, and t = the time. When the jet is flying downwind, it is flying in the same direction as the wind, so it flys faster than the still airspeed. When it is flying upwind, it is flying in the opposite direction from the wind (against the wind), so in this case the wind slows down the plane. In table format, this is:
__Formula: ( Rate ) x (Time)= (Distance)
Downwind: (340 + w) x ( t ) = ( 200 )
__Upwind: (340 - w) x ( t ) = ( 140 )
To solve, notice that the times are the same. Rewrite the distance equation to solve for "t":
t = d / r
t = 200 / (340 + w)
t = 140 / (340 - w)
Now set the two equations (above) equal to each other and solve for w:
200 / (340 + w) = 140 / (340 - w)
200 (340 - w) = 140 (340 + w)
68000 - 200w = 47600 + 140w
20400 = 340w
w = 60 mph
To check your work, calculate the time for the downwind and upwind conditions:
Downwind time = 200 / (340 + 60) = 0.5 hours
Upwind time = 140 / (340 - 60) = 0.5 hours
The two times are the same (as stated in the original problem), so our answer is correct.
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