SOLUTION: Can someone please help me with the following problem? A plane has a cruising speed of 280 miles per hour and the wind velocity is 40 miles per hour. How far can the plane fly a

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Question 166412: Can someone please help me with the following problem?
A plane has a cruising speed of 280 miles per hour and the wind velocity is 40 miles per hour. How far can the plane fly and return in 7 hours?
So far I have begun to make a chart to help solve the problem, but I am just very confused.
Found 2 solutions by scott8148, gonzo:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
d=rt __ distance out is the same as distance back

the total time is 7hr __ if t is the time out, then 7-t is the time back

rate with the wind is 280+40 or 320

rate back is 280-40 or 240

320 * t = 240 * (7-t) __ 320t=1680-240t __ 560t=1680 __ t=3

substituting __ d=320(3) __ d=960 (one way)

Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
let D = distance going.
let D = distance coming back.
let x = amount of time to get there.
let y = amount of time to get back.
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assume the wind velocity is with the plane going and against the plane coming back.
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rate of speed going is 280 mph of the plane plus 40 mph of the wind = 320 mph.
rate of speed coming back is 280 mph of the plane minus 40 mph of the wind = 240 mph.
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rate times time = distance
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equation for going is:
320*x = D (equation 1)**********************
equation for coming back is:
240*y = D (equation 2)*********************
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since they both equal D, then they are equal to each other.
320*x = 240*y
solve for y
y = 320*x/240 = (4/3)*x
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total time going and coming back is 7 hours.
x + y = 7
since y = (4/3)*x, equation becomes:
x + (4/3)*x = 7
multiply both sides of equation by 3:
3*x + 4*x = 21
simplify:
7*x = 21
x = 3
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if x = 3, then y = 4, since x + y = 7
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plug into original equations 1 and 2.
equation 1:
320*3 = D
D = 960 miles
equation 2:
240*4 = D
D = 960
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the plane flies 960 miles to get there and 960 miles to get back for a total of 1920 miles.