SOLUTION: A plane flies 435 miles with the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 15mph, find the speed of the plane in still air.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A plane flies 435 miles with the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 15mph, find the speed of the plane in still air.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 428014: A plane flies 435 miles with the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 15mph, find the speed of the plane in still air.
Found 4 solutions by mananth, ikleyn, timofer, greenestamps:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
Deleted . Thanks to the tutor


Answer by ikleyn(53419) About Me  (Show Source):
You can put this solution on YOUR website!
.
A plane flies 435 miles with the wind and 345 miles against the wind in the same length of time.
If the speed of the wind is 15 mph, find the speed of the plane in still air.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


        The solution in the post by @manath is incorrect.
        I came to bring a correct solution. 


let speed in still air be x mph
wind speed 15 mph  (given).

..

against wind x - 15 mph
with    wind x + 15 mph


Distance against   wind 345
Distance with tail wind 435


    Write the "time" equation



345 /(x- 15) = 435 /(x+15)    (1)

345 *(x+ 15) = 435 *(x- 15)

345 x + 345*15 = 435 x - 435*15

345*15 + 435*15 = 435x - 345x

11700 = 90x

x = 11700/90 = 130 mph.


ANSWER.  The speed of the plane in still air is 130 mph.


CHECK.  Let's check time (equation (1)):  345/115 = 3 hours;  435/145 = 3 hours.  ! correct !

Solved correctly.



Answer by timofer(136) About Me  (Show Source):
You can put this solution on YOUR website!
rate x time = distance
time = distance/rate

Take speed without wind as s.
Those with wind and against wind times given as equal.

With the wind 435%2F%28s%2B15%29
Against the wind 345%2F%28s-15%29

Times were equal.
435%2F%28s%2B15%29=345%2F%28s-15%29
Solve this for s.

435%28s-15%29=345%28s%2B15%29
87%28s-15%29=69%28s%2B15%29
87s-1305=69s%2B1035
%2887-69%29s=1305%2B1035
18s=2340
s=2340%2F18=1170%2F9=130
130 miles per hour without the wind

Answer by greenestamps(13258) About Me  (Show Source):
You can put this solution on YOUR website!


An informal solution using logical reasoning instead of formal algebra....

The speed with the wind is 15mph greater than the speed of the plane in still air; the speed against the wind is 15mph less than the speed of the plane in still air. So the difference between the speed with the wind and the speed against the wind is 30mph.

The difference in the distances at the two speeds (in equal amounts of time) is 435-345 = 90 miles; so the time at each speed is 90/30 = 3 hours.

So the speed with the wind is 435/3 = 145mph and the speed against the wind is 345/3 = 115mph.

Then you have three choices for finding the speed of the plane in still air:
(1) 115+15 = 130mph
(2) 145-15 = 130mph
(3) halfway between 115mph and 145mph = 130mph

ANSWER: 130mph

-----------------------------------------------------------

(Note that the numbers you need to work with are "nicer" than those needed in either of the formal algebraic solutions....)