SOLUTION: Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 97 km/h faster than the other. If the two planes are 12,344 kilometers apart a

Let slower airplane's speed, be S

Then faster airplane's speed = S + 97

We then get the following DISTANCE equation: 8S + 8(S + 97) = 12,344

8S + 8S + 8(97) = 12,344 

16S = 12,344 - 8(97)

Speed of slower airplane, or 

Now, add 97 to the slower speed to get the faster! 

Let "r" be the rate of the slower plane, in miles per hour.

Then the rate of the faster plane is (r+97) mph.


The total distance equation is


    12344 = 8r + 8*(r+97)


Simplify and solve


    r + (r+97) = 12344/8 = 1543

    2r                   = 1543-97 = 1446

     r                             = 1446/2 = 723.


ANSWER.  The rates of the planes are  723 mph  and  723+97 = 820 mph.