SOLUTION: An airplane flies 410 miles with the wind and 310 against the wind in the same length of time. If the speed of the wind is 40, what is the speed of the airplane in still air? A.)

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Question 994514: An airplane flies 410 miles with the wind and 310 against the wind in the same length of time. If the speed of the wind is 40, what is the speed of the airplane in still air?
A.). 293mph. B). 288mph. C). 124mph. D). 278mph

I have tried this:
X=d/t.
X=410 -40
X=370
X=310+40
X=350
Found 2 solutions by macston, josgarithmetic:
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
.
t=time; d=distance; r=rate
t=d/r
.
With wind:
t=410mi/r+40
Against wind:
t=310mi/r-40
.
Since time in both directions is the same:
410mi/r+40=310mi/r-40
410(r-40)=310(r+40)
410r-16400=310r+12400
100r=28800
r=288
.
ANSWER: The rate of the plane in still air is 288 mph.

Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
Assign some variables.


Uniform Rates Travel Rule, RT=D to relate rate, time, distance;
also can be used as R=D/T. 
Direction   speed        time       distance
WITH        r+w           t          m
AGAINST     r-w           t          n

See that the same number in the same variable t is used for both directions. The question asks for r, but not for t.
Direction   speed        time              distance
WITH        r+w           t=m/(r+w)          m
AGAINST     r-w           t=n/(r-w)          n


Equate the two formulas for time t:

This equation uses only one unknown variable, r, which is what the question asks to find. Solve the equation for r.
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