SOLUTION: An airplane averages 150 mph. If a trip from Atlanta to Charleston takes 2 hours 48 minutes going against the wind, and 2 hours on on the return flight going with the wind, what is

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Question 1197567: An airplane averages 150 mph. If a trip from Atlanta to Charleston takes 2 hours 48 minutes going against the wind, and 2 hours on on the return flight going with the wind, what is the speed of the wind
Found 4 solutions by math_tutor2020, greenestamps, josgarithmetic, ikleyn:
Answer by math_tutor2020(3817) About Me  (Show Source):
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w = speed of the wind in mph

2 hrs + 48 min = 2 hrs + (48/60) hrs
2 hrs + 48 min = 2 hrs + 0.8 hrs
2 hrs + 48 min = 2.8 hrs

150-w = speed of the plane going against the wind
distance = rate*time
distance = (150-w)*2.8
distance = 420-2.8w

150+w = speed of the plane going with the wind
distance = rate*time
distance = (150+w)*2
distance = 300+2w

The distance is same each time because the plane is following the same route, when going from Atlanta to Charleston then back from Charleston to Atlanta.

Because the distance is the same for each equation, we can equate the right hand sides and solve for w.
420-2.8w = 300+2w
420-300 = 2w+2.8w
120 = 4.8w
w = 120/4.8
w = 25
The speed of the wind is 25 mph

Check:
If the plane goes against the wind, then its speed is 150-w = 150-25 = 125 mph.
Traveling for 2.8 hours means it covers a distance of 125*2.8 = 350 miles
If the plane goes with the wind, then its speed is 150+w = 150+25 = 175 mph.
Traveling for 2 hours gives a distance of 175*2 = 350 miles.
We get the same distance each time to help confirm the answer.

Answer: 25 mph

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a very unorthodox solution method -- in case you are interested in looking at alternatives.

Let x be the speed of the wind; then the plane's speeds are 150+x with the wind and 150-x against the wind.

The distances are the same, so the ratio of speeds is the reciprocal of the ratio of the times. The ratio of the two times in minutes is 168/120 = 7/5. So

%28150%2Bx%29%2F%28150-x%29=7%2F5
5%28150%2Bx%29=7%28150-x%29
750%2B5x=1050-7x
12x=300
x=25

ANSWER: The wind speed is 25mph

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
                 SPEED           TIME         DISTANCE

A to C           r-w=d/2.8       2.8            d

C to A           r+w=d/2         2.0            d

Total                            4.8           2d

Average, for round trip, given as 150 mph.
2d%2F4.8=150
d=%284.8%2A150%29%2F2
d=2.4%2A150
d=360
-
system%282.8%28r-w%29=360%2C2%28r%2Bw%29=360%29
system%28r-w=128.571428%2Cr%2Bw=180%29

system%28r=154.285714%2Cw=25.714286%29

Close enough to highlight%28w=26%29

Answer by ikleyn(52878) About Me  (Show Source):
You can put this solution on YOUR website!
.

The solution by @josgarithmetic is conceptually  TOTALLY  wrong.

It is wrong,  since this airplane averages  150 mph in  STILL  AIR
(the part of the condition,  which is  highlight%28highlight%28MISSED%29%29  in the post).

Again :   150 mph is the average speed of the plane in  STILL  AIR,
but  NOT  IN  THIS  round trip:  150 mph relates to  TOTALLY  DIFFERENT  conception.


        The post itself has a  HUGE  DEFICIENCY:  it missed
        to determine correctly all the participating values/conditions.


Taking it into the consideration, the problem, as it is worded in the post,
is ambiguous, which is not allowed for Math problems.


Therefore,  my advise to the visitor is to throw this  " problem "  to the closest garbage bin
and to  highlight%28highlight%28MEMORIZE%29%29  that only mathematically correct problems are the subject of consideration at this forum.


            Each correct mathematical problem is a piece of art.
        What is not piece of art - is not a correct mathematical problem.


Exactly as the wife of an emperor should be beyond suspicions,
every  Math problem must be ideally and absolutely correct - always.