SOLUTION: It took a plane 2 hours to fly form Dallas to New York with the headwind and 1.5 hours to return with the tailwind. If the wind speed was 30 mph, how far apart are the two cities?

Question 1197152: It took a plane 2 hours to fly form Dallas to New York with the headwind and 1.5 hours to return with the tailwind. If the wind speed was 30 mph, how far apart are the two cities?
Answer by ikleyn(52801) (Show Source): You can put this solution on YOUR website!
.
It took a plane 2 hours to fly form Dallas to New York with the headwind
and 1.5 hours to return with the tailwind. If the wind speed was 30 mph,
how far apart are the two cities?
~~~~~~~~~~~~~~~

Let x be the plane' speed in still air.

Then you can write these equation

    2*(x-30) = 1.5*(x+30).


Each side of the equation is the distance between the cities, and the equation
says that two distance are the same in each direction.


Simplify equation and find x

    2x - 60   = 1.5x + 45

    2x - 1.5x = 45 + 60

      0.5x    =   105

         x    =   105/0.5 = 210.


Thus the speed of the plane in still air is 210 miles per hour.


The effective speed with the wind is 210 + 30 = 240 miles per hours.


The distance between the cities in this problem is 1.5*240 = 360 miles.    ANSWER

Solved.

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I think, there is no need to explain that in real life, the distance between the real cities is greater.

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